(5x-1)(5x+1)-(5x+2)2=35

Solution for (5x-1)(5x+1)-(5x+2)2=35 equation:

Simplifying
(5x + -1)(5x + 1) + -1(5x + 2) * 2 = 35

Reorder the terms:
(-1 + 5x)(5x + 1) + -1(5x + 2) * 2 = 35

Reorder the terms:
(-1 + 5x)(1 + 5x) + -1(5x + 2) * 2 = 35

Multiply (-1 + 5x) * (1 + 5x)
(-1(1 + 5x) + 5x * (1 + 5x)) + -1(5x + 2) * 2 = 35
((1 * -1 + 5x * -1) + 5x * (1 + 5x)) + -1(5x + 2) * 2 = 35
((-1 + -5x) + 5x * (1 + 5x)) + -1(5x + 2) * 2 = 35
(-1 + -5x + (1 * 5x + 5x * 5x)) + -1(5x + 2) * 2 = 35
(-1 + -5x + (5x + 25x2)) + -1(5x + 2) * 2 = 35

Combine like terms: -5x + 5x = 0
(-1 + 0 + 25x2) + -1(5x + 2) * 2 = 35
(-1 + 25x2) + -1(5x + 2) * 2 = 35

Reorder the terms:
-1 + 25x2 + -1(2 + 5x) * 2 = 35

Reorder the terms for easier multiplication:
-1 + 25x2 + -1 * 2(2 + 5x) = 35

Multiply -1 * 2
-1 + 25x2 + -2(2 + 5x) = 35
-1 + 25x2 + (2 * -2 + 5x * -2) = 35
-1 + 25x2 + (-4 + -10x) = 35

Reorder the terms:
-1 + -4 + -10x + 25x2 = 35

Combine like terms: -1 + -4 = -5
-5 + -10x + 25x2 = 35

Solving
-5 + -10x + 25x2 = 35

Solving for variable 'x'.

Reorder the terms:
-5 + -35 + -10x + 25x2 = 35 + -35

Combine like terms: -5 + -35 = -40
-40 + -10x + 25x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-40 + -10x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -2x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-8 + -2x + 5x2)' equal to zero and attempt to solve:

Simplifying
-8 + -2x + 5x2 = 0

Solving
-8 + -2x + 5x2 = 0

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

Divide each side by '5'.
-1.6 + -0.4x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -0.4x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -0.4x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -0.4x + x2 = 0 + 1.6
-0.4x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-0.4x + x2 = 1.6

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 1.6 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + -0.4x + x2 = 1.64

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1
x + -0.2 = 1.280624847

Simplifying
x + -0.2 = 1.280624847

Reorder the terms:
-0.2 + x = 1.280624847

Solving
-0.2 + x = 1.280624847

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = 1.280624847 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = 1.280624847 + 0.2
x = 1.280624847 + 0.2

Combine like terms: 1.280624847 + 0.2 = 1.480624847
x = 1.480624847

Simplifying
x = 1.480624847

Subproblem 2
x + -0.2 = -1.280624847

Simplifying
x + -0.2 = -1.280624847

Reorder the terms:
-0.2 + x = -1.280624847

Solving
-0.2 + x = -1.280624847

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = -1.280624847 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = -1.280624847 + 0.2
x = -1.280624847 + 0.2

Combine like terms: -1.280624847 + 0.2 = -1.080624847
x = -1.080624847

Simplifying
x = -1.080624847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.480624847, -1.080624847}
Solution
x = {1.480624847, -1.080624847}