6(2x^2-15x-126)=0

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Solution for 6(2x^2-15x-126)=0 equation: 


Simplifying
6(2x2 + -15x + -126) = 0

Reorder the terms:
6(-126 + -15x + 2x2) = 0
(-126 * 6 + -15x * 6 + 2x2 * 6) = 0
(-756 + -90x + 12x2) = 0

Solving
-756 + -90x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-126 + -15x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-126 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-126 + -15x + 2x2 = 0

Solving
-126 + -15x + 2x2 = 0

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

Divide each side by '2'.
-63 + -7.5x + x2 = 0

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + -7.5x + 63 + x2 = 0 + 63

Reorder the terms:
-63 + 63 + -7.5x + x2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -7.5x + x2 = 0 + 63
-7.5x + x2 = 0 + 63

Combine like terms: 0 + 63 = 63
-7.5x + x2 = 63

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 63 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 63 + 14.0625

Combine like terms: 63 + 14.0625 = 77.0625
14.0625 + -7.5x + x2 = 77.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 77.0625

Calculate the square root of the right side: 8.778524933

Break this problem into two subproblems by setting 
(x + -3.75) equal to 8.778524933 and -8.778524933.


Subproblem 1
x + -3.75 = 8.778524933

Simplifying
x + -3.75 = 8.778524933

Reorder the terms:
-3.75 + x = 8.778524933

Solving
-3.75 + x = 8.778524933

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 8.778524933 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 8.778524933 + 3.75
x = 8.778524933 + 3.75

Combine like terms: 8.778524933 + 3.75 = 12.528524933
x = 12.528524933

Simplifying
x = 12.528524933


Subproblem 2
x + -3.75 = -8.778524933

Simplifying
x + -3.75 = -8.778524933

Reorder the terms:
-3.75 + x = -8.778524933

Solving
-3.75 + x = -8.778524933

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -8.778524933 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -8.778524933 + 3.75
x = -8.778524933 + 3.75

Combine like terms: -8.778524933 + 3.75 = -5.028524933
x = -5.028524933

Simplifying
x = -5.028524933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.528524933, -5.028524933}
Solution
x = {12.528524933, -5.028524933}

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