80=2(2x+3)2(x-2)

Solution for 80=2(2x+3)2(x-2) equation:

Simplifying
80 = 2(2x + 3) * 2(x + -2)

Reorder the terms:
80 = 2(3 + 2x) * 2(x + -2)

Reorder the terms:
80 = 2(3 + 2x) * 2(-2 + x)

Reorder the terms for easier multiplication:
80 = 2 * 2(3 + 2x)(-2 + x)

Multiply 2 * 2
80 = 4(3 + 2x)(-2 + x)

Multiply (3 + 2x) * (-2 + x)
80 = 4(3(-2 + x) + 2x * (-2 + x))
80 = 4((-2 * 3 + x * 3) + 2x * (-2 + x))
80 = 4((-6 + 3x) + 2x * (-2 + x))
80 = 4(-6 + 3x + (-2 * 2x + x * 2x))
80 = 4(-6 + 3x + (-4x + 2x2))

Combine like terms: 3x + -4x = -1x
80 = 4(-6 + -1x + 2x2)
80 = (-6 * 4 + -1x * 4 + 2x2 * 4)
80 = (-24 + -4x + 8x2)

Solving
80 = -24 + -4x + 8x2

Solving for variable 'x'.

Combine like terms: 80 + 24 = 104
104 + 4x + -8x2 = -24 + -4x + 8x2 + 24 + 4x + -8x2

Reorder the terms:
104 + 4x + -8x2 = -24 + 24 + -4x + 4x + 8x2 + -8x2

Combine like terms: -24 + 24 = 0
104 + 4x + -8x2 = 0 + -4x + 4x + 8x2 + -8x2
104 + 4x + -8x2 = -4x + 4x + 8x2 + -8x2

Combine like terms: -4x + 4x = 0
104 + 4x + -8x2 = 0 + 8x2 + -8x2
104 + 4x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
104 + 4x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(26 + x + -2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(26 + x + -2x2)' equal to zero and attempt to solve:

Simplifying
26 + x + -2x2 = 0

Solving
26 + x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-13 + -0.5x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -0.5x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -0.5x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -0.5x + x2 = 0 + 13
-0.5x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-0.5x + x2 = 13

The x term is x.  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.
-0.5x + 0.25 + x2 = 13 + 0.25

Reorder the terms:
0.25 + -0.5x + x2 = 13 + 0.25

Combine like terms: 13 + 0.25 = 13.25
0.25 + -0.5x + x2 = 13.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
x + 0.5 = 3.640054945

Simplifying
x + 0.5 = 3.640054945

Reorder the terms:
0.5 + x = 3.640054945

Solving
0.5 + x = 3.640054945

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 = 3.640054945 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.640054945 + -0.5
x = 3.640054945 + -0.5

Combine like terms: 3.640054945 + -0.5 = 3.140054945
x = 3.140054945

Simplifying
x = 3.140054945

Subproblem 2
x + 0.5 = -3.640054945

Simplifying
x + 0.5 = -3.640054945

Reorder the terms:
0.5 + x = -3.640054945

Solving
0.5 + x = -3.640054945

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 = -3.640054945 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.640054945 + -0.5
x = -3.640054945 + -0.5

Combine like terms: -3.640054945 + -0.5 = -4.140054945
x = -4.140054945

Simplifying
x = -4.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.140054945, -4.140054945}
Solution
x = {3.140054945, -4.140054945}