(x+4)(2x+2)=(3x)(20-2x)+(2x-52)

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Solution for (x+4)(2x+2)=(3x)(20-2x)+(2x-52) equation: 


Simplifying
(x + 4)(2x + 2) = (3x)(20 + -2x) + (2x + -52)

Reorder the terms:
(4 + x)(2x + 2) = (3x)(20 + -2x) + (2x + -52)

Reorder the terms:
(4 + x)(2 + 2x) = (3x)(20 + -2x) + (2x + -52)

Multiply (4 + x) * (2 + 2x)
(4(2 + 2x) + x(2 + 2x)) = (3x)(20 + -2x) + (2x + -52)
((2 * 4 + 2x * 4) + x(2 + 2x)) = (3x)(20 + -2x) + (2x + -52)
((8 + 8x) + x(2 + 2x)) = (3x)(20 + -2x) + (2x + -52)
(8 + 8x + (2 * x + 2x * x)) = (3x)(20 + -2x) + (2x + -52)
(8 + 8x + (2x + 2x2)) = (3x)(20 + -2x) + (2x + -52)

Combine like terms: 8x + 2x = 10x
(8 + 10x + 2x2) = (3x)(20 + -2x) + (2x + -52)

Remove parenthesis around (3x)
8 + 10x + 2x2 = 3x(20 + -2x) + (2x + -52)
8 + 10x + 2x2 = (20 * 3x + -2x * 3x) + (2x + -52)
8 + 10x + 2x2 = (60x + -6x2) + (2x + -52)

Reorder the terms:
8 + 10x + 2x2 = 60x + -6x2 + (-52 + 2x)

Remove parenthesis around (-52 + 2x)
8 + 10x + 2x2 = 60x + -6x2 + -52 + 2x

Reorder the terms:
8 + 10x + 2x2 = -52 + 60x + 2x + -6x2

Combine like terms: 60x + 2x = 62x
8 + 10x + 2x2 = -52 + 62x + -6x2

Solving
8 + 10x + 2x2 = -52 + 62x + -6x2

Solving for variable 'x'.

Reorder the terms:
8 + 52 + 10x + -62x + 2x2 + 6x2 = -52 + 62x + -6x2 + 52 + -62x + 6x2

Combine like terms: 8 + 52 = 60
60 + 10x + -62x + 2x2 + 6x2 = -52 + 62x + -6x2 + 52 + -62x + 6x2

Combine like terms: 10x + -62x = -52x
60 + -52x + 2x2 + 6x2 = -52 + 62x + -6x2 + 52 + -62x + 6x2

Combine like terms: 2x2 + 6x2 = 8x2
60 + -52x + 8x2 = -52 + 62x + -6x2 + 52 + -62x + 6x2

Reorder the terms:
60 + -52x + 8x2 = -52 + 52 + 62x + -62x + -6x2 + 6x2

Combine like terms: -52 + 52 = 0
60 + -52x + 8x2 = 0 + 62x + -62x + -6x2 + 6x2
60 + -52x + 8x2 = 62x + -62x + -6x2 + 6x2

Combine like terms: 62x + -62x = 0
60 + -52x + 8x2 = 0 + -6x2 + 6x2
60 + -52x + 8x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
60 + -52x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -13x + 2x2) = 0

Factor a trinomial.
4((3 + -2x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, 5}

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