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

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


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

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

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

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

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

Reorder the terms:
-6 + -1x + x2 = -3(-3 + x)
-6 + -1x + x2 = (-3 * -3 + x * -3)
-6 + -1x + x2 = (9 + -3x)

Solving
-6 + -1x + x2 = 9 + -3x

Solving for variable 'x'.

Reorder the terms:
-6 + -9 + -1x + 3x + x2 = 9 + -3x + -9 + 3x

Combine like terms: -6 + -9 = -15
-15 + -1x + 3x + x2 = 9 + -3x + -9 + 3x

Combine like terms: -1x + 3x = 2x
-15 + 2x + x2 = 9 + -3x + -9 + 3x

Reorder the terms:
-15 + 2x + x2 = 9 + -9 + -3x + 3x

Combine like terms: 9 + -9 = 0
-15 + 2x + x2 = 0 + -3x + 3x
-15 + 2x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-15 + 2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 3}

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