5(x+3)(x+7)=(x+3)(2x-13)

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Solution for 5(x+3)(x+7)=(x+3)(2x-13) equation: 


Simplifying
5(x + 3)(x + 7) = (x + 3)(2x + -13)

Reorder the terms:
5(3 + x)(x + 7) = (x + 3)(2x + -13)

Reorder the terms:
5(3 + x)(7 + x) = (x + 3)(2x + -13)

Multiply (3 + x) * (7 + x)
5(3(7 + x) + x(7 + x)) = (x + 3)(2x + -13)
5((7 * 3 + x * 3) + x(7 + x)) = (x + 3)(2x + -13)
5((21 + 3x) + x(7 + x)) = (x + 3)(2x + -13)
5(21 + 3x + (7 * x + x * x)) = (x + 3)(2x + -13)
5(21 + 3x + (7x + x2)) = (x + 3)(2x + -13)

Combine like terms: 3x + 7x = 10x
5(21 + 10x + x2) = (x + 3)(2x + -13)
(21 * 5 + 10x * 5 + x2 * 5) = (x + 3)(2x + -13)
(105 + 50x + 5x2) = (x + 3)(2x + -13)

Reorder the terms:
105 + 50x + 5x2 = (3 + x)(2x + -13)

Reorder the terms:
105 + 50x + 5x2 = (3 + x)(-13 + 2x)

Multiply (3 + x) * (-13 + 2x)
105 + 50x + 5x2 = (3(-13 + 2x) + x(-13 + 2x))
105 + 50x + 5x2 = ((-13 * 3 + 2x * 3) + x(-13 + 2x))
105 + 50x + 5x2 = ((-39 + 6x) + x(-13 + 2x))
105 + 50x + 5x2 = (-39 + 6x + (-13 * x + 2x * x))
105 + 50x + 5x2 = (-39 + 6x + (-13x + 2x2))

Combine like terms: 6x + -13x = -7x
105 + 50x + 5x2 = (-39 + -7x + 2x2)

Solving
105 + 50x + 5x2 = -39 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
105 + 39 + 50x + 7x + 5x2 + -2x2 = -39 + -7x + 2x2 + 39 + 7x + -2x2

Combine like terms: 105 + 39 = 144
144 + 50x + 7x + 5x2 + -2x2 = -39 + -7x + 2x2 + 39 + 7x + -2x2

Combine like terms: 50x + 7x = 57x
144 + 57x + 5x2 + -2x2 = -39 + -7x + 2x2 + 39 + 7x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
144 + 57x + 3x2 = -39 + -7x + 2x2 + 39 + 7x + -2x2

Reorder the terms:
144 + 57x + 3x2 = -39 + 39 + -7x + 7x + 2x2 + -2x2

Combine like terms: -39 + 39 = 0
144 + 57x + 3x2 = 0 + -7x + 7x + 2x2 + -2x2
144 + 57x + 3x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
144 + 57x + 3x2 = 0 + 2x2 + -2x2
144 + 57x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
144 + 57x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(48 + 19x + x2) = 0

Factor a trinomial.
3((16 + x)(3 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16

Subproblem 2
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
Solution
x = {-16, -3}

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