Solve for a -7a^2b^2=(-7ab)

$- 7 a^{2} b^{2} = (- 7 a b)$

Step 1

Add $7 a b$ to both sides of the equation.

$- 7 a^{2} b^{2} + 7 a b = 0$

Step 2

Factor $7 a b$ out of $- 7 a^{2} b^{2} + 7 a b$ .

Factor $7 a b$ out of $- 7 a^{2} b^{2}$ .

$7 a b (- a b) + 7 a b = 0$

Factor $7 a b$ out of $7 a b$ .

$7 a b (- a b) + 7 a b (1) = 0$

Factor $7 a b$ out of $7 a b (- a b) + 7 a b (1)$ .

$7 a b (- a b + 1) = 0$

Step 3

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

$a = 0$

$- a b + 1 = 0$

Step 4

Set $a$ equal to $0$ .

$a = 0$

Step 5

Set $- a b + 1$ equal to $0$ and solve for $a$ .

Set $- a b + 1$ equal to $0$ .

$- a b + 1 = 0$

Solve $- a b + 1 = 0$ for $a$ .

Subtract $1$ from both sides of the equation.

$- a b = - 1$

Divide each term in $- a b = - 1$ by $- 1 b$ and simplify.

Divide each term in $- a b = - 1$ by $- 1 b$ .

$\frac{- a b}{- 1 b} = \frac{- 1}{- 1 b}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{a b}{b} = \frac{- 1}{- 1 b}$

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{a b}{b} = \frac{- 1}{- 1 b}$

Divide $a$ by $1$ .

$a = \frac{- 1}{- 1 b}$

Simplify the right side.

Dividing two negative values results in a positive value.

$a = \frac{1}{b}$

Step 6

The final solution is all the values that make $7 a b (- a b + 1) = 0$ true.

$a = 0$

$a = \frac{1}{b}$