Solve for y -5y^2+7y+6=0

$- 5 y^{2} + 7 y + 6 = 0$

Step 1

Factor the left side of the equation.

Factor $- 1$ out of $- 5 y^{2} + 7 y + 6$ .

Factor $- 1$ out of $- 5 y^{2}$ .

$- (5 y^{2}) + 7 y + 6 = 0$

Factor $- 1$ out of $7 y$ .

$- (5 y^{2}) - (- 7 y) + 6 = 0$

Rewrite $6$ as $- 1 (- 6)$ .

$- (5 y^{2}) - (- 7 y) - 1 \cdot - 6 = 0$

Factor $- 1$ out of $- (5 y^{2}) - (- 7 y)$ .

$- (5 y^{2} - 7 y) - 1 \cdot - 6 = 0$

Factor $- 1$ out of $- (5 y^{2} - 7 y) - 1 (- 6)$ .

$- (5 y^{2} - 7 y - 6) = 0$

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot - 6 = - 30$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 y$ .

$- (5 y^{2} - 7 y - 6) = 0$

Rewrite $- 7$ as $3$ plus $- 10$

$- (5 y^{2} + (3 - 10) y - 6) = 0$

Apply the distributive property.

$- (5 y^{2} + 3 y - 10 y - 6) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((5 y^{2} + 3 y) - 10 y - 6) = 0$

Factor out the greatest common factor (GCF) from each group.

$- (y (5 y + 3) - 2 (5 y + 3)) = 0$

Factor the polynomial by factoring out the greatest common factor, $5 y + 3$ .

$- ((5 y + 3) (y - 2)) = 0$

Remove unnecessary parentheses.

$- (5 y + 3) (y - 2) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$5 y + 3 = 0$

$y - 2 = 0$

Step 3

Set $5 y + 3$ equal to $0$ and solve for $y$ .

Set $5 y + 3$ equal to $0$ .

$5 y + 3 = 0$

Solve $5 y + 3 = 0$ for $y$ .

Subtract $3$ from both sides of the equation.

$5 y = - 3$

Divide each term in $5 y = - 3$ by $5$ and simplify.

Divide each term in $5 y = - 3$ by $5$ .

$\frac{5 y}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 3}{5}$

Divide $y$ by $1$ .

$y = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{3}{5}$

Step 4

Set $y - 2$ equal to $0$ and solve for $y$ .

Set $y - 2$ equal to $0$ .

$y - 2 = 0$

Add $2$ to both sides of the equation.

$y = 2$

Step 5

The final solution is all the values that make $- (5 y + 3) (y - 2) = 0$ true.

$y = - \frac{3}{5}, 2$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{3}{5}, 2$

Decimal Form:

$y = - 0.6, 2$

Solve for y -5y^2+7y+6=0

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