15x^2-12x-135=0

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Solution for 15x^2-12x-135=0 equation: 


Simplifying
15x2 + -12x + -135 = 0

Reorder the terms:
-135 + -12x + 15x2 = 0

Solving
-135 + -12x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-45 + -4x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-45 + -4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-45 + -4x + 5x2 = 0

Solving
-45 + -4x + 5x2 = 0

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

Divide each side by '5'.
-9 + -0.8x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -0.8x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -0.8x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -0.8x + x2 = 0 + 9
-0.8x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-0.8x + x2 = 9

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 9 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 9 + 0.16

Combine like terms: 9 + 0.16 = 9.16
0.16 + -0.8x + x2 = 9.16

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 9.16

Calculate the square root of the right side: 3.02654919

Break this problem into two subproblems by setting 
(x + -0.4) equal to 3.02654919 and -3.02654919.


Subproblem 1
x + -0.4 = 3.02654919

Simplifying
x + -0.4 = 3.02654919

Reorder the terms:
-0.4 + x = 3.02654919

Solving
-0.4 + x = 3.02654919

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 3.02654919 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 3.02654919 + 0.4
x = 3.02654919 + 0.4

Combine like terms: 3.02654919 + 0.4 = 3.42654919
x = 3.42654919

Simplifying
x = 3.42654919


Subproblem 2
x + -0.4 = -3.02654919

Simplifying
x + -0.4 = -3.02654919

Reorder the terms:
-0.4 + x = -3.02654919

Solving
-0.4 + x = -3.02654919

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -3.02654919 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -3.02654919 + 0.4
x = -3.02654919 + 0.4

Combine like terms: -3.02654919 + 0.4 = -2.62654919
x = -2.62654919

Simplifying
x = -2.62654919


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.42654919, -2.62654919}
Solution
x = {3.42654919, -2.62654919}

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