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

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

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

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

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

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = -4(x + 3)
((3 * -2 + x * -2) + x(3 + x)) = -4(x + 3)
((-6 + -2x) + x(3 + x)) = -4(x + 3)
(-6 + -2x + (3 * x + x * x)) = -4(x + 3)
(-6 + -2x + (3x + x2)) = -4(x + 3)

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = -4(x + 3)

Reorder the terms:
-6 + 1x + x2 = -4(3 + x)
-6 + 1x + x2 = (3 * -4 + x * -4)
-6 + 1x + x2 = (-12 + -4x)

Solving
-6 + 1x + x2 = -12 + -4x

Solving for variable 'x'.

Reorder the terms:
-6 + 12 + 1x + 4x + x2 = -12 + -4x + 12 + 4x

Combine like terms: -6 + 12 = 6
6 + 1x + 4x + x2 = -12 + -4x + 12 + 4x

Combine like terms: 1x + 4x = 5x
6 + 5x + x2 = -12 + -4x + 12 + 4x

Reorder the terms:
6 + 5x + x2 = -12 + 12 + -4x + 4x

Combine like terms: -12 + 12 = 0
6 + 5x + x2 = 0 + -4x + 4x
6 + 5x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
6 + 5x + x2 = 0

Factor a trinomial.
(3 + x)(2 + x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-3, -2}