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

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

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

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

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

Multiply (-2 + x) * (5 + x)
4(-2(5 + x) + x(5 + x)) = 4x + -2
4((5 * -2 + x * -2) + x(5 + x)) = 4x + -2
4((-10 + -2x) + x(5 + x)) = 4x + -2
4(-10 + -2x + (5 * x + x * x)) = 4x + -2
4(-10 + -2x + (5x + x2)) = 4x + -2

Combine like terms: -2x + 5x = 3x
4(-10 + 3x + x2) = 4x + -2
(-10 * 4 + 3x * 4 + x2 * 4) = 4x + -2
(-40 + 12x + 4x2) = 4x + -2

Reorder the terms:
-40 + 12x + 4x2 = -2 + 4x

Solving
-40 + 12x + 4x2 = -2 + 4x

Solving for variable 'x'.

Reorder the terms:
-40 + 2 + 12x + -4x + 4x2 = -2 + 4x + 2 + -4x

Combine like terms: -40 + 2 = -38
-38 + 12x + -4x + 4x2 = -2 + 4x + 2 + -4x

Combine like terms: 12x + -4x = 8x
-38 + 8x + 4x2 = -2 + 4x + 2 + -4x

Reorder the terms:
-38 + 8x + 4x2 = -2 + 2 + 4x + -4x

Combine like terms: -2 + 2 = 0
-38 + 8x + 4x2 = 0 + 4x + -4x
-38 + 8x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-38 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 4x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
-19 + 4x + 2x2 = 0

Solving
-19 + 4x + 2x2 = 0

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

Divide each side by '2'.
-9.5 + 2x + x2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 2x + 9.5 + x2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 2x + x2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 2x + x2 = 0 + 9.5
2x + x2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
2x + x2 = 9.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 9.5 + 1

Reorder the terms:
1 + 2x + x2 = 9.5 + 1

Combine like terms: 9.5 + 1 = 10.5
1 + 2x + x2 = 10.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10.5

Calculate the square root of the right side: 3.240370349

Break this problem into two subproblems by setting 
(x + 1) equal to 3.240370349 and -3.240370349.

Subproblem 1
x + 1 = 3.240370349

Simplifying
x + 1 = 3.240370349

Reorder the terms:
1 + x = 3.240370349

Solving
1 + x = 3.240370349

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.240370349 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.240370349 + -1
x = 3.240370349 + -1

Combine like terms: 3.240370349 + -1 = 2.240370349
x = 2.240370349

Simplifying
x = 2.240370349

Subproblem 2
x + 1 = -3.240370349

Simplifying
x + 1 = -3.240370349

Reorder the terms:
1 + x = -3.240370349

Solving
1 + x = -3.240370349

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.240370349 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.240370349 + -1
x = -3.240370349 + -1

Combine like terms: -3.240370349 + -1 = -4.240370349
x = -4.240370349

Simplifying
x = -4.240370349

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.240370349, -4.240370349}
Solution
x = {2.240370349, -4.240370349}