(2x+2)(2x-4)=60

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Solution for (2x+2)(2x-4)=60 equation: 


Simplifying
(2x + 2)(2x + -4) = 60

Reorder the terms:
(2 + 2x)(2x + -4) = 60

Reorder the terms:
(2 + 2x)(-4 + 2x) = 60

Multiply (2 + 2x) * (-4 + 2x)
(2(-4 + 2x) + 2x * (-4 + 2x)) = 60
((-4 * 2 + 2x * 2) + 2x * (-4 + 2x)) = 60
((-8 + 4x) + 2x * (-4 + 2x)) = 60
(-8 + 4x + (-4 * 2x + 2x * 2x)) = 60
(-8 + 4x + (-8x + 4x2)) = 60

Combine like terms: 4x + -8x = -4x
(-8 + -4x + 4x2) = 60

Solving
-8 + -4x + 4x2 = 60

Solving for variable 'x'.

Reorder the terms:
-8 + -60 + -4x + 4x2 = 60 + -60

Combine like terms: -8 + -60 = -68
-68 + -4x + 4x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-68 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-17 + -1x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-17 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + -1x + x2 = 0

Solving
-17 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -1x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -1x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x + x2 = 0 + 17
-1x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-1x + x2 = 17

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 17 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 17 + 0.25

Combine like terms: 17 + 0.25 = 17.25
0.25 + -1x + x2 = 17.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + -0.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + -0.5 = 4.153311931

Simplifying
x + -0.5 = 4.153311931

Reorder the terms:
-0.5 + x = 4.153311931

Solving
-0.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 4.153311931 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 4.153311931 + 0.5
x = 4.153311931 + 0.5

Combine like terms: 4.153311931 + 0.5 = 4.653311931
x = 4.653311931

Simplifying
x = 4.653311931


Subproblem 2
x + -0.5 = -4.153311931

Simplifying
x + -0.5 = -4.153311931

Reorder the terms:
-0.5 + x = -4.153311931

Solving
-0.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -4.153311931 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -4.153311931 + 0.5
x = -4.153311931 + 0.5

Combine like terms: -4.153311931 + 0.5 = -3.653311931
x = -3.653311931

Simplifying
x = -3.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.653311931, -3.653311931}
Solution
x = {4.653311931, -3.653311931}

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