(6x+5)(6x+5)=175

Solution for (6x+5)(6x+5)=175 equation:

Simplifying
(6x + 5)(6x + 5) = 175

Reorder the terms:
(5 + 6x)(6x + 5) = 175

Reorder the terms:
(5 + 6x)(5 + 6x) = 175

Multiply (5 + 6x) * (5 + 6x)
(5(5 + 6x) + 6x * (5 + 6x)) = 175
((5 * 5 + 6x * 5) + 6x * (5 + 6x)) = 175
((25 + 30x) + 6x * (5 + 6x)) = 175
(25 + 30x + (5 * 6x + 6x * 6x)) = 175
(25 + 30x + (30x + 36x2)) = 175

Combine like terms: 30x + 30x = 60x
(25 + 60x + 36x2) = 175

Solving
25 + 60x + 36x2 = 175

Solving for variable 'x'.

Reorder the terms:
25 + -175 + 60x + 36x2 = 175 + -175

Combine like terms: 25 + -175 = -150
-150 + 60x + 36x2 = 175 + -175

Combine like terms: 175 + -175 = 0
-150 + 60x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-25 + 10x + 6x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-25 + 10x + 6x2)' equal to zero and attempt to solve:

Simplifying
-25 + 10x + 6x2 = 0

Solving
-25 + 10x + 6x2 = 0

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

Divide each side by '6'.
-4.166666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 1.666666667x + 4.166666667 + x2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 1.666666667x + x2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 4.166666667
1.666666667x + x2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
1.666666667x + x2 = 4.166666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 4.166666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 4.166666667 + 0.6944444447

Combine like terms: 4.166666667 + 0.6944444447 = 4.8611111117
0.6944444447 + 1.666666667x + x2 = 4.8611111117

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 4.8611111117

Calculate the square root of the right side: 2.204792759

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.204792759 and -2.204792759.

Subproblem 1
x + 0.8333333335 = 2.204792759

Simplifying
x + 0.8333333335 = 2.204792759

Reorder the terms:
0.8333333335 + x = 2.204792759

Solving
0.8333333335 + x = 2.204792759

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 2.204792759 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 2.204792759 + -0.8333333335
x = 2.204792759 + -0.8333333335

Combine like terms: 2.204792759 + -0.8333333335 = 1.3714594255
x = 1.3714594255

Simplifying
x = 1.3714594255

Subproblem 2
x + 0.8333333335 = -2.204792759

Simplifying
x + 0.8333333335 = -2.204792759

Reorder the terms:
0.8333333335 + x = -2.204792759

Solving
0.8333333335 + x = -2.204792759

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -2.204792759 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -2.204792759 + -0.8333333335
x = -2.204792759 + -0.8333333335

Combine like terms: -2.204792759 + -0.8333333335 = -3.0381260925
x = -3.0381260925

Simplifying
x = -3.0381260925

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3714594255, -3.0381260925}
Solution
x = {1.3714594255, -3.0381260925}