15x*15x=15(x+1)(x+1)

Solution for 15x*15x=15(x+1)(x+1) equation:

Simplifying
15x * 15x = 15(x + 1)(x + 1)

Reorder the terms for easier multiplication:
15 * 15x * x = 15(x + 1)(x + 1)

Multiply 15 * 15
225x * x = 15(x + 1)(x + 1)

Multiply x * x
225x2 = 15(x + 1)(x + 1)

Reorder the terms:
225x2 = 15(1 + x)(x + 1)

Reorder the terms:
225x2 = 15(1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
225x2 = 15(1(1 + x) + x(1 + x))
225x2 = 15((1 * 1 + x * 1) + x(1 + x))
225x2 = 15((1 + 1x) + x(1 + x))
225x2 = 15(1 + 1x + (1 * x + x * x))
225x2 = 15(1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
225x2 = 15(1 + 2x + x2)
225x2 = (1 * 15 + 2x * 15 + x2 * 15)
225x2 = (15 + 30x + 15x2)

Solving
225x2 = 15 + 30x + 15x2

Solving for variable 'x'.

Reorder the terms:
-15 + -30x + 225x2 + -15x2 = 15 + 30x + 15x2 + -15 + -30x + -15x2

Combine like terms: 225x2 + -15x2 = 210x2
-15 + -30x + 210x2 = 15 + 30x + 15x2 + -15 + -30x + -15x2

Reorder the terms:
-15 + -30x + 210x2 = 15 + -15 + 30x + -30x + 15x2 + -15x2

Combine like terms: 15 + -15 = 0
-15 + -30x + 210x2 = 0 + 30x + -30x + 15x2 + -15x2
-15 + -30x + 210x2 = 30x + -30x + 15x2 + -15x2

Combine like terms: 30x + -30x = 0
-15 + -30x + 210x2 = 0 + 15x2 + -15x2
-15 + -30x + 210x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-15 + -30x + 210x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-1 + -2x + 14x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-1 + -2x + 14x2)' equal to zero and attempt to solve:

Simplifying
-1 + -2x + 14x2 = 0

Solving
-1 + -2x + 14x2 = 0

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

Divide each side by '14'.
-0.07142857143 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.07142857143' to each side of the equation.
-0.07142857143 + -0.1428571429x + 0.07142857143 + x2 = 0 + 0.07142857143

Reorder the terms:
-0.07142857143 + 0.07142857143 + -0.1428571429x + x2 = 0 + 0.07142857143

Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000
0.00000000000 + -0.1428571429x + x2 = 0 + 0.07142857143
-0.1428571429x + x2 = 0 + 0.07142857143

Combine like terms: 0 + 0.07142857143 = 0.07142857143
-0.1428571429x + x2 = 0.07142857143

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 0.07142857143 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.07142857143 + 0.005102040819

Combine like terms: 0.07142857143 + 0.005102040819 = 0.076530612249
0.005102040819 + -0.1428571429x + x2 = 0.076530612249

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.076530612249

Calculate the square root of the right side: 0.276641668

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.276641668 and -0.276641668.

Subproblem 1
x + -0.07142857145 = 0.276641668

Simplifying
x + -0.07142857145 = 0.276641668

Reorder the terms:
-0.07142857145 + x = 0.276641668

Solving
-0.07142857145 + x = 0.276641668

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = 0.276641668 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = 0.276641668 + 0.07142857145
x = 0.276641668 + 0.07142857145

Combine like terms: 0.276641668 + 0.07142857145 = 0.34807023945
x = 0.34807023945

Simplifying
x = 0.34807023945

Subproblem 2
x + -0.07142857145 = -0.276641668

Simplifying
x + -0.07142857145 = -0.276641668

Reorder the terms:
-0.07142857145 + x = -0.276641668

Solving
-0.07142857145 + x = -0.276641668

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = -0.276641668 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = -0.276641668 + 0.07142857145
x = -0.276641668 + 0.07142857145

Combine like terms: -0.276641668 + 0.07142857145 = -0.20521309655
x = -0.20521309655

Simplifying
x = -0.20521309655

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.34807023945, -0.20521309655}
Solution
x = {0.34807023945, -0.20521309655}