(6x-5)(6x-5)=36x-25

Solution for (6x-5)(6x-5)=36x-25 equation:

Simplifying
(6x + -5)(6x + -5) = 36x + -25

Reorder the terms:
(-5 + 6x)(6x + -5) = 36x + -25

Reorder the terms:
(-5 + 6x)(-5 + 6x) = 36x + -25

Multiply (-5 + 6x) * (-5 + 6x)
(-5(-5 + 6x) + 6x * (-5 + 6x)) = 36x + -25
((-5 * -5 + 6x * -5) + 6x * (-5 + 6x)) = 36x + -25
((25 + -30x) + 6x * (-5 + 6x)) = 36x + -25
(25 + -30x + (-5 * 6x + 6x * 6x)) = 36x + -25
(25 + -30x + (-30x + 36x2)) = 36x + -25

Combine like terms: -30x + -30x = -60x
(25 + -60x + 36x2) = 36x + -25

Reorder the terms:
25 + -60x + 36x2 = -25 + 36x

Solving
25 + -60x + 36x2 = -25 + 36x

Solving for variable 'x'.

Reorder the terms:
25 + 25 + -60x + -36x + 36x2 = -25 + 36x + 25 + -36x

Combine like terms: 25 + 25 = 50
50 + -60x + -36x + 36x2 = -25 + 36x + 25 + -36x

Combine like terms: -60x + -36x = -96x
50 + -96x + 36x2 = -25 + 36x + 25 + -36x

Reorder the terms:
50 + -96x + 36x2 = -25 + 25 + 36x + -36x

Combine like terms: -25 + 25 = 0
50 + -96x + 36x2 = 0 + 36x + -36x
50 + -96x + 36x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
50 + -96x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -48x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(25 + -48x + 18x2)' equal to zero and attempt to solve:

Simplifying
25 + -48x + 18x2 = 0

Solving
25 + -48x + 18x2 = 0

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

Divide each side by '18'.
1.388888889 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.388888889' to each side of the equation.
1.388888889 + -2.666666667x + -1.388888889 + x2 = 0 + -1.388888889

Reorder the terms:
1.388888889 + -1.388888889 + -2.666666667x + x2 = 0 + -1.388888889

Combine like terms: 1.388888889 + -1.388888889 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + -1.388888889
-2.666666667x + x2 = 0 + -1.388888889

Combine like terms: 0 + -1.388888889 = -1.388888889
-2.666666667x + x2 = -1.388888889

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -1.388888889 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -1.388888889 + 1.777777780

Combine like terms: -1.388888889 + 1.777777780 = 0.388888891
1.777777780 + -2.666666667x + x2 = 0.388888891

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 0.388888891

Calculate the square root of the right side: 0.623609566

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 0.623609566 and -0.623609566.

Subproblem 1
x + -1.333333334 = 0.623609566

Simplifying
x + -1.333333334 = 0.623609566

Reorder the terms:
-1.333333334 + x = 0.623609566

Solving
-1.333333334 + x = 0.623609566

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 0.623609566 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 0.623609566 + 1.333333334
x = 0.623609566 + 1.333333334

Combine like terms: 0.623609566 + 1.333333334 = 1.9569429
x = 1.9569429

Simplifying
x = 1.9569429

Subproblem 2
x + -1.333333334 = -0.623609566

Simplifying
x + -1.333333334 = -0.623609566

Reorder the terms:
-1.333333334 + x = -0.623609566

Solving
-1.333333334 + x = -0.623609566

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -0.623609566 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -0.623609566 + 1.333333334
x = -0.623609566 + 1.333333334

Combine like terms: -0.623609566 + 1.333333334 = 0.709723768
x = 0.709723768

Simplifying
x = 0.709723768

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.9569429, 0.709723768}
Solution
x = {1.9569429, 0.709723768}