3x+33-6=(5x+2)(5x+2)

Solution for 3x+33-6=(5x+2)(5x+2) equation:

Simplifying
3x + 33 + -6 = (5x + 2)(5x + 2)

Reorder the terms:
33 + -6 + 3x = (5x + 2)(5x + 2)

Combine like terms: 33 + -6 = 27
27 + 3x = (5x + 2)(5x + 2)

Reorder the terms:
27 + 3x = (2 + 5x)(5x + 2)

Reorder the terms:
27 + 3x = (2 + 5x)(2 + 5x)

Multiply (2 + 5x) * (2 + 5x)
27 + 3x = (2(2 + 5x) + 5x * (2 + 5x))
27 + 3x = ((2 * 2 + 5x * 2) + 5x * (2 + 5x))
27 + 3x = ((4 + 10x) + 5x * (2 + 5x))
27 + 3x = (4 + 10x + (2 * 5x + 5x * 5x))
27 + 3x = (4 + 10x + (10x + 25x2))

Combine like terms: 10x + 10x = 20x
27 + 3x = (4 + 20x + 25x2)

Solving
27 + 3x = 4 + 20x + 25x2

Solving for variable 'x'.

Reorder the terms:
27 + -4 + 3x + -20x + -25x2 = 4 + 20x + 25x2 + -4 + -20x + -25x2

Combine like terms: 27 + -4 = 23
23 + 3x + -20x + -25x2 = 4 + 20x + 25x2 + -4 + -20x + -25x2

Combine like terms: 3x + -20x = -17x
23 + -17x + -25x2 = 4 + 20x + 25x2 + -4 + -20x + -25x2

Reorder the terms:
23 + -17x + -25x2 = 4 + -4 + 20x + -20x + 25x2 + -25x2

Combine like terms: 4 + -4 = 0
23 + -17x + -25x2 = 0 + 20x + -20x + 25x2 + -25x2
23 + -17x + -25x2 = 20x + -20x + 25x2 + -25x2

Combine like terms: 20x + -20x = 0
23 + -17x + -25x2 = 0 + 25x2 + -25x2
23 + -17x + -25x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
23 + -17x + -25x2 = 0

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
-0.92 + 0.68x + x2 = 0

Move the constant term to the right:

Add '0.92' to each side of the equation.
-0.92 + 0.68x + 0.92 + x2 = 0 + 0.92

Reorder the terms:
-0.92 + 0.92 + 0.68x + x2 = 0 + 0.92

Combine like terms: -0.92 + 0.92 = 0.00
0.00 + 0.68x + x2 = 0 + 0.92
0.68x + x2 = 0 + 0.92

Combine like terms: 0 + 0.92 = 0.92
0.68x + x2 = 0.92

The x term is 0.68x.  Take half its coefficient (0.34).
Square it (0.1156) and add it to both sides.

Add '0.1156' to each side of the equation.
0.68x + 0.1156 + x2 = 0.92 + 0.1156

Reorder the terms:
0.1156 + 0.68x + x2 = 0.92 + 0.1156

Combine like terms: 0.92 + 0.1156 = 1.0356
0.1156 + 0.68x + x2 = 1.0356

Factor a perfect square on the left side:
(x + 0.34)(x + 0.34) = 1.0356

Calculate the square root of the right side: 1.017644339

Break this problem into two subproblems by setting 
(x + 0.34) equal to 1.017644339 and -1.017644339.

Subproblem 1
x + 0.34 = 1.017644339

Simplifying
x + 0.34 = 1.017644339

Reorder the terms:
0.34 + x = 1.017644339

Solving
0.34 + x = 1.017644339

Solving for variable 'x'.

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

Add '-0.34' to each side of the equation.
0.34 + -0.34 + x = 1.017644339 + -0.34

Combine like terms: 0.34 + -0.34 = 0.00
0.00 + x = 1.017644339 + -0.34
x = 1.017644339 + -0.34

Combine like terms: 1.017644339 + -0.34 = 0.677644339
x = 0.677644339

Simplifying
x = 0.677644339

Subproblem 2
x + 0.34 = -1.017644339

Simplifying
x + 0.34 = -1.017644339

Reorder the terms:
0.34 + x = -1.017644339

Solving
0.34 + x = -1.017644339

Solving for variable 'x'.

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

Add '-0.34' to each side of the equation.
0.34 + -0.34 + x = -1.017644339 + -0.34

Combine like terms: 0.34 + -0.34 = 0.00
0.00 + x = -1.017644339 + -0.34
x = -1.017644339 + -0.34

Combine like terms: -1.017644339 + -0.34 = -1.357644339
x = -1.357644339

Simplifying
x = -1.357644339

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.677644339, -1.357644339}