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

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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.
(-3 + -1x)(7 + -1x) = 0


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 '(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
Solution
x = {-3, 7}

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