4(x+1)2-2(2x-5)(x+2)=0

Solution for 4(x+1)2-2(2x-5)(x+2)=0 equation:

Simplifying
4(x + 1) * 2 + -2(2x + -5)(x + 2) = 0

Reorder the terms:
4(1 + x) * 2 + -2(2x + -5)(x + 2) = 0

Reorder the terms for easier multiplication:
4 * 2(1 + x) + -2(2x + -5)(x + 2) = 0

Multiply 4 * 2
8(1 + x) + -2(2x + -5)(x + 2) = 0
(1 * 8 + x * 8) + -2(2x + -5)(x + 2) = 0
(8 + 8x) + -2(2x + -5)(x + 2) = 0

Reorder the terms:
8 + 8x + -2(-5 + 2x)(x + 2) = 0

Reorder the terms:
8 + 8x + -2(-5 + 2x)(2 + x) = 0

Multiply (-5 + 2x) * (2 + x)
8 + 8x + -2(-5(2 + x) + 2x * (2 + x)) = 0
8 + 8x + -2((2 * -5 + x * -5) + 2x * (2 + x)) = 0
8 + 8x + -2((-10 + -5x) + 2x * (2 + x)) = 0
8 + 8x + -2(-10 + -5x + (2 * 2x + x * 2x)) = 0
8 + 8x + -2(-10 + -5x + (4x + 2x2)) = 0

Combine like terms: -5x + 4x = -1x
8 + 8x + -2(-10 + -1x + 2x2) = 0
8 + 8x + (-10 * -2 + -1x * -2 + 2x2 * -2) = 0
8 + 8x + (20 + 2x + -4x2) = 0

Reorder the terms:
8 + 20 + 8x + 2x + -4x2 = 0

Combine like terms: 8 + 20 = 28
28 + 8x + 2x + -4x2 = 0

Combine like terms: 8x + 2x = 10x
28 + 10x + -4x2 = 0

Solving
28 + 10x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 5x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(14 + 5x + -2x2)' equal to zero and attempt to solve:

Simplifying
14 + 5x + -2x2 = 0

Solving
14 + 5x + -2x2 = 0

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

Divide each side by '-2'.
-7 + -2.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -2.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2.5x + x2 = 0 + 7
-2.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2.5x + x2 = 7

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 7 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 7 + 1.5625

Combine like terms: 7 + 1.5625 = 8.5625
1.5625 + -2.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.926174978 and -2.926174978.

Subproblem 1
x + -1.25 = 2.926174978

Simplifying
x + -1.25 = 2.926174978

Reorder the terms:
-1.25 + x = 2.926174978

Solving
-1.25 + x = 2.926174978

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.926174978 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.926174978 + 1.25
x = 2.926174978 + 1.25

Combine like terms: 2.926174978 + 1.25 = 4.176174978
x = 4.176174978

Simplifying
x = 4.176174978

Subproblem 2
x + -1.25 = -2.926174978

Simplifying
x + -1.25 = -2.926174978

Reorder the terms:
-1.25 + x = -2.926174978

Solving
-1.25 + x = -2.926174978

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.926174978 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.926174978 + 1.25
x = -2.926174978 + 1.25

Combine like terms: -2.926174978 + 1.25 = -1.676174978
x = -1.676174978

Simplifying
x = -1.676174978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.176174978, -1.676174978}
Solution
x = {4.176174978, -1.676174978}