Solve for x 12-x(x-3)=(6-x)(x+2)

$12 - x (x - 3) = (6 - x) (x + 2)$

Simplify each term.

Apply the distributive property.

$12 - x \cdot x - x \cdot - 3 = (6 - x) (x + 2)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$12 - (x \cdot x) - x \cdot - 3 = (6 - x) (x + 2)$

Multiply $x$ by $x$ .

$12 - x^{2} - x \cdot - 3 = (6 - x) (x + 2)$

Multiply $- 3$ by $- 1$ .

$12 - x^{2} + 3 x = (6 - x) (x + 2)$

Simplify $(6 - x) (x + 2)$ .

Expand $(6 - x) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$12 - x^{2} + 3 x = 6 (x + 2) - x (x + 2)$

Apply the distributive property.

$12 - x^{2} + 3 x = 6 x + 6 \cdot 2 - x (x + 2)$

Apply the distributive property.

$12 - x^{2} + 3 x = 6 x + 6 \cdot 2 - x \cdot x - x \cdot 2$

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $2$ .

$12 - x^{2} + 3 x = 6 x + 12 - x \cdot x - x \cdot 2$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$12 - x^{2} + 3 x = 6 x + 12 - (x \cdot x) - x \cdot 2$

Multiply $x$ by $x$ .

$12 - x^{2} + 3 x = 6 x + 12 - x^{2} - x \cdot 2$

Multiply $2$ by $- 1$ .

$12 - x^{2} + 3 x = 6 x + 12 - x^{2} - 2 x$

Subtract $2 x$ from $6 x$ .

$12 - x^{2} + 3 x = 4 x + 12 - x^{2}$

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$12 - x^{2} + 3 x - 4 x = 12 - x^{2}$

Add $x^{2}$ to both sides of the equation.

$12 - x^{2} + 3 x - 4 x + x^{2} = 12$

Combine the opposite terms in $12 - x^{2} + 3 x - 4 x + x^{2}$ .

Add $- x^{2}$ and $x^{2}$ .

$12 + 3 x - 4 x + 0 = 12$

Add $12 + 3 x - 4 x$ and $0$ .

$12 + 3 x - 4 x = 12$

Subtract $4 x$ from $3 x$ .

$12 - x = 12$

Move all terms not containing $x$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$- x = 12 - 12$

Subtract $12$ from $12$ .

$- x = 0$

Divide each term in $- x = 0$ by $- 1$ and simplify.

Divide each term in $- x = 0$ by $- 1$ .

$\frac{- x}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{0}{- 1}$

Divide $x$ by $1$ .

$x = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x = 0$

Solve for x 12-x(x-3)=(6-x)(x+2)

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