(x-3)(x+2)=-5(x-3)

Solution for (x-3)(x+2)=-5(x-3) equation:

Simplifying
(x + -3)(x + 2) = -5(x + -3)

Reorder the terms:
(-3 + x)(x + 2) = -5(x + -3)

Reorder the terms:
(-3 + x)(2 + x) = -5(x + -3)

Multiply (-3 + x) * (2 + x)
(-3(2 + x) + x(2 + x)) = -5(x + -3)
((2 * -3 + x * -3) + x(2 + x)) = -5(x + -3)
((-6 + -3x) + x(2 + x)) = -5(x + -3)
(-6 + -3x + (2 * x + x * x)) = -5(x + -3)
(-6 + -3x + (2x + x2)) = -5(x + -3)

Combine like terms: -3x + 2x = -1x
(-6 + -1x + x2) = -5(x + -3)

Reorder the terms:
-6 + -1x + x2 = -5(-3 + x)
-6 + -1x + x2 = (-3 * -5 + x * -5)
-6 + -1x + x2 = (15 + -5x)

Solving
-6 + -1x + x2 = 15 + -5x

Solving for variable 'x'.

Reorder the terms:
-6 + -15 + -1x + 5x + x2 = 15 + -5x + -15 + 5x

Combine like terms: -6 + -15 = -21
-21 + -1x + 5x + x2 = 15 + -5x + -15 + 5x

Combine like terms: -1x + 5x = 4x
-21 + 4x + x2 = 15 + -5x + -15 + 5x

Reorder the terms:
-21 + 4x + x2 = 15 + -15 + -5x + 5x

Combine like terms: 15 + -15 = 0
-21 + 4x + x2 = 0 + -5x + 5x
-21 + 4x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-21 + 4x + x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
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 = {-7, 3}