15x*15x-27x-6=0

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Solution for 15x*15x-27x-6=0 equation: 


Simplifying
15x * 15x + -27x + -6 = 0

Reorder the terms for easier multiplication:
15 * 15x * x + -27x + -6 = 0

Multiply 15 * 15
225x * x + -27x + -6 = 0

Multiply x * x
225x2 + -27x + -6 = 0

Reorder the terms:
-6 + -27x + 225x2 = 0

Solving
-6 + -27x + 225x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -9x + 75x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -9x + 75x2)' equal to zero and attempt to solve:

Simplifying
-2 + -9x + 75x2 = 0

Solving
-2 + -9x + 75x2 = 0

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

Divide each side by '75'.
-0.02666666667 + -0.12x + x2 = 0

Move the constant term to the right:

Add '0.02666666667' to each side of the equation.
-0.02666666667 + -0.12x + 0.02666666667 + x2 = 0 + 0.02666666667

Reorder the terms:
-0.02666666667 + 0.02666666667 + -0.12x + x2 = 0 + 0.02666666667

Combine like terms: -0.02666666667 + 0.02666666667 = 0.00000000000
0.00000000000 + -0.12x + x2 = 0 + 0.02666666667
-0.12x + x2 = 0 + 0.02666666667

Combine like terms: 0 + 0.02666666667 = 0.02666666667
-0.12x + x2 = 0.02666666667

The x term is -0.12x.  Take half its coefficient (-0.06).
Square it (0.0036) and add it to both sides.

Add '0.0036' to each side of the equation.
-0.12x + 0.0036 + x2 = 0.02666666667 + 0.0036

Reorder the terms:
0.0036 + -0.12x + x2 = 0.02666666667 + 0.0036

Combine like terms: 0.02666666667 + 0.0036 = 0.03026666667
0.0036 + -0.12x + x2 = 0.03026666667

Factor a perfect square on the left side:
(x + -0.06)(x + -0.06) = 0.03026666667

Calculate the square root of the right side: 0.173973178

Break this problem into two subproblems by setting 
(x + -0.06) equal to 0.173973178 and -0.173973178.


Subproblem 1
x + -0.06 = 0.173973178

Simplifying
x + -0.06 = 0.173973178

Reorder the terms:
-0.06 + x = 0.173973178

Solving
-0.06 + x = 0.173973178

Solving for variable 'x'.

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

Add '0.06' to each side of the equation.
-0.06 + 0.06 + x = 0.173973178 + 0.06

Combine like terms: -0.06 + 0.06 = 0.00
0.00 + x = 0.173973178 + 0.06
x = 0.173973178 + 0.06

Combine like terms: 0.173973178 + 0.06 = 0.233973178
x = 0.233973178

Simplifying
x = 0.233973178


Subproblem 2
x + -0.06 = -0.173973178

Simplifying
x + -0.06 = -0.173973178

Reorder the terms:
-0.06 + x = -0.173973178

Solving
-0.06 + x = -0.173973178

Solving for variable 'x'.

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

Add '0.06' to each side of the equation.
-0.06 + 0.06 + x = -0.173973178 + 0.06

Combine like terms: -0.06 + 0.06 = 0.00
0.00 + x = -0.173973178 + 0.06
x = -0.173973178 + 0.06

Combine like terms: -0.173973178 + 0.06 = -0.113973178
x = -0.113973178

Simplifying
x = -0.113973178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.233973178, -0.113973178}
Solution
x = {0.233973178, -0.113973178}

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