4x(5x+6)=2(2x-2)

Solution for 4x(5x+6)=2(2x-2) equation:

Simplifying
4x(5x + 6) = 2(2x + -2)

Reorder the terms:
4x(6 + 5x) = 2(2x + -2)
(6 * 4x + 5x * 4x) = 2(2x + -2)
(24x + 20x2) = 2(2x + -2)

Reorder the terms:
24x + 20x2 = 2(-2 + 2x)
24x + 20x2 = (-2 * 2 + 2x * 2)
24x + 20x2 = (-4 + 4x)

Solving
24x + 20x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:
4 + 24x + -4x + 20x2 = -4 + 4x + 4 + -4x

Combine like terms: 24x + -4x = 20x
4 + 20x + 20x2 = -4 + 4x + 4 + -4x

Reorder the terms:
4 + 20x + 20x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
4 + 20x + 20x2 = 0 + 4x + -4x
4 + 20x + 20x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
4 + 20x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 5x + 5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 5x + 5x2)' equal to zero and attempt to solve:

Simplifying
1 + 5x + 5x2 = 0

Solving
1 + 5x + 5x2 = 0

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

Divide each side by '5'.
0.2 + x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x + x2 = 0 + -0.2
x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
x + x2 = -0.2

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.
 + 0.25 + x2 = -0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
1.25 + x2 = 0.05

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.223606798 and -0.223606798.

Subproblem 1
x + 0.5 = 0.223606798

Simplifying
x + 0.5 = 0.223606798

Reorder the terms:
0.5 + x = 0.223606798

Solving
0.5 + x = 0.223606798

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 = 0.223606798 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.223606798 + -0.5
x = 0.223606798 + -0.5

Combine like terms: 0.223606798 + -0.5 = -0.276393202
x = -0.276393202

Simplifying
x = -0.276393202

Subproblem 2
x + 0.5 = -0.223606798

Simplifying
x + 0.5 = -0.223606798

Reorder the terms:
0.5 + x = -0.223606798

Solving
0.5 + x = -0.223606798

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 = -0.223606798 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.223606798 + -0.5
x = -0.223606798 + -0.5

Combine like terms: -0.223606798 + -0.5 = -0.723606798
x = -0.723606798

Simplifying
x = -0.723606798

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.276393202, -0.723606798}
Solution
x = {-0.276393202, -0.723606798}