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

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


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

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

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

Multiply (-5 + x) * (3 + 2x)
(-5(3 + 2x) + x(3 + 2x)) = -3(x + -5)
((3 * -5 + 2x * -5) + x(3 + 2x)) = -3(x + -5)
((-15 + -10x) + x(3 + 2x)) = -3(x + -5)
(-15 + -10x + (3 * x + 2x * x)) = -3(x + -5)
(-15 + -10x + (3x + 2x2)) = -3(x + -5)

Combine like terms: -10x + 3x = -7x
(-15 + -7x + 2x2) = -3(x + -5)

Reorder the terms:
-15 + -7x + 2x2 = -3(-5 + x)
-15 + -7x + 2x2 = (-5 * -3 + x * -3)
-15 + -7x + 2x2 = (15 + -3x)

Solving
-15 + -7x + 2x2 = 15 + -3x

Solving for variable 'x'.

Reorder the terms:
-15 + -15 + -7x + 3x + 2x2 = 15 + -3x + -15 + 3x

Combine like terms: -15 + -15 = -30
-30 + -7x + 3x + 2x2 = 15 + -3x + -15 + 3x

Combine like terms: -7x + 3x = -4x
-30 + -4x + 2x2 = 15 + -3x + -15 + 3x

Reorder the terms:
-30 + -4x + 2x2 = 15 + -15 + -3x + 3x

Combine like terms: 15 + -15 = 0
-30 + -4x + 2x2 = 0 + -3x + 3x
-30 + -4x + 2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-30 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -2x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-3, 5}

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