(2x-5)2(4x+7)=2

Solution for (2x-5)2(4x+7)=2 equation:

Simplifying
(2x + -5) * 2(4x + 7) = 2

Reorder the terms:
(-5 + 2x) * 2(4x + 7) = 2

Reorder the terms:
(-5 + 2x) * 2(7 + 4x) = 2

Reorder the terms for easier multiplication:
2(-5 + 2x)(7 + 4x) = 2

Multiply (-5 + 2x) * (7 + 4x)
2(-5(7 + 4x) + 2x * (7 + 4x)) = 2
2((7 * -5 + 4x * -5) + 2x * (7 + 4x)) = 2
2((-35 + -20x) + 2x * (7 + 4x)) = 2
2(-35 + -20x + (7 * 2x + 4x * 2x)) = 2
2(-35 + -20x + (14x + 8x2)) = 2

Combine like terms: -20x + 14x = -6x
2(-35 + -6x + 8x2) = 2
(-35 * 2 + -6x * 2 + 8x2 * 2) = 2
(-70 + -12x + 16x2) = 2

Solving
-70 + -12x + 16x2 = 2

Solving for variable 'x'.

Reorder the terms:
-70 + -2 + -12x + 16x2 = 2 + -2

Combine like terms: -70 + -2 = -72
-72 + -12x + 16x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-72 + -12x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -3x + 4x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-18 + -3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-18 + -3x + 4x2 = 0

Solving
-18 + -3x + 4x2 = 0

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

Divide each side by '4'.
-4.5 + -0.75x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -0.75x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -0.75x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -0.75x + x2 = 0 + 4.5
-0.75x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-0.75x + x2 = 4.5

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 4.5 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 4.5 + 0.140625

Combine like terms: 4.5 + 0.140625 = 4.640625
0.140625 + -0.75x + x2 = 4.640625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 4.640625

Calculate the square root of the right side: 2.154210992

Break this problem into two subproblems by setting 
(x + -0.375) equal to 2.154210992 and -2.154210992.

Subproblem 1
x + -0.375 = 2.154210992

Simplifying
x + -0.375 = 2.154210992

Reorder the terms:
-0.375 + x = 2.154210992

Solving
-0.375 + x = 2.154210992

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 2.154210992 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 2.154210992 + 0.375
x = 2.154210992 + 0.375

Combine like terms: 2.154210992 + 0.375 = 2.529210992
x = 2.529210992

Simplifying
x = 2.529210992

Subproblem 2
x + -0.375 = -2.154210992

Simplifying
x + -0.375 = -2.154210992

Reorder the terms:
-0.375 + x = -2.154210992

Solving
-0.375 + x = -2.154210992

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -2.154210992 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -2.154210992 + 0.375
x = -2.154210992 + 0.375

Combine like terms: -2.154210992 + 0.375 = -1.779210992
x = -1.779210992

Simplifying
x = -1.779210992

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.529210992, -1.779210992}
Solution
x = {2.529210992, -1.779210992}