4(2x-3)(5x+2)=64

Solution for 4(2x-3)(5x+2)=64 equation:

Simplifying
4(2x + -3)(5x + 2) = 64

Reorder the terms:
4(-3 + 2x)(5x + 2) = 64

Reorder the terms:
4(-3 + 2x)(2 + 5x) = 64

Multiply (-3 + 2x) * (2 + 5x)
4(-3(2 + 5x) + 2x * (2 + 5x)) = 64
4((2 * -3 + 5x * -3) + 2x * (2 + 5x)) = 64
4((-6 + -15x) + 2x * (2 + 5x)) = 64
4(-6 + -15x + (2 * 2x + 5x * 2x)) = 64
4(-6 + -15x + (4x + 10x2)) = 64

Combine like terms: -15x + 4x = -11x
4(-6 + -11x + 10x2) = 64
(-6 * 4 + -11x * 4 + 10x2 * 4) = 64
(-24 + -44x + 40x2) = 64

Solving
-24 + -44x + 40x2 = 64

Solving for variable 'x'.

Reorder the terms:
-24 + -64 + -44x + 40x2 = 64 + -64

Combine like terms: -24 + -64 = -88
-88 + -44x + 40x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-88 + -44x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-22 + -11x + 10x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-22 + -11x + 10x2)' equal to zero and attempt to solve:

Simplifying
-22 + -11x + 10x2 = 0

Solving
-22 + -11x + 10x2 = 0

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

Divide each side by '10'.
-2.2 + -1.1x + x2 = 0.0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -1.1x + 2.2 + x2 = 0.0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -1.1x + x2 = 0.0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.1x + x2 = 0.0 + 2.2
-1.1x + x2 = 0.0 + 2.2

Combine like terms: 0.0 + 2.2 = 2.2
-1.1x + x2 = 2.2

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = 2.2 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = 2.2 + 0.3025

Combine like terms: 2.2 + 0.3025 = 2.5025
0.3025 + -1.1x + x2 = 2.5025

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 2.5025

Calculate the square root of the right side: 1.581929202

Break this problem into two subproblems by setting 
(x + -0.55) equal to 1.581929202 and -1.581929202.

Subproblem 1
x + -0.55 = 1.581929202

Simplifying
x + -0.55 = 1.581929202

Reorder the terms:
-0.55 + x = 1.581929202

Solving
-0.55 + x = 1.581929202

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = 1.581929202 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 1.581929202 + 0.55
x = 1.581929202 + 0.55

Combine like terms: 1.581929202 + 0.55 = 2.131929202
x = 2.131929202

Simplifying
x = 2.131929202

Subproblem 2
x + -0.55 = -1.581929202

Simplifying
x + -0.55 = -1.581929202

Reorder the terms:
-0.55 + x = -1.581929202

Solving
-0.55 + x = -1.581929202

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = -1.581929202 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -1.581929202 + 0.55
x = -1.581929202 + 0.55

Combine like terms: -1.581929202 + 0.55 = -1.031929202
x = -1.031929202

Simplifying
x = -1.031929202

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.131929202, -1.031929202}
Solution
x = {2.131929202, -1.031929202}