(x-3)(x+4)=-2(x-3)

Solution for (x-3)(x+4)=-2(x-3) equation:

Simplifying
(x + -3)(x + 4) = -2(x + -3)

Reorder the terms:
(-3 + x)(x + 4) = -2(x + -3)

Reorder the terms:
(-3 + x)(4 + x) = -2(x + -3)

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = -2(x + -3)
((4 * -3 + x * -3) + x(4 + x)) = -2(x + -3)
((-12 + -3x) + x(4 + x)) = -2(x + -3)
(-12 + -3x + (4 * x + x * x)) = -2(x + -3)
(-12 + -3x + (4x + x2)) = -2(x + -3)

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = -2(x + -3)

Reorder the terms:
-12 + 1x + x2 = -2(-3 + x)
-12 + 1x + x2 = (-3 * -2 + x * -2)
-12 + 1x + x2 = (6 + -2x)

Solving
-12 + 1x + x2 = 6 + -2x

Solving for variable 'x'.

Reorder the terms:
-12 + -6 + 1x + 2x + x2 = 6 + -2x + -6 + 2x

Combine like terms: -12 + -6 = -18
-18 + 1x + 2x + x2 = 6 + -2x + -6 + 2x

Combine like terms: 1x + 2x = 3x
-18 + 3x + x2 = 6 + -2x + -6 + 2x

Reorder the terms:
-18 + 3x + x2 = 6 + -6 + -2x + 2x

Combine like terms: 6 + -6 = 0
-18 + 3x + x2 = 0 + -2x + 2x
-18 + 3x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-18 + 3x + x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-6, 3}