4x^2-8x-12=6x

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Solution for 4x^2-8x-12=6x equation: 


Simplifying
4x2 + -8x + -12 = 6x

Reorder the terms:
-12 + -8x + 4x2 = 6x

Solving
-12 + -8x + 4x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-12 + -8x + -6x + 4x2 = 6x + -6x

Combine like terms: -8x + -6x = -14x
-12 + -14x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-12 + -14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-6 + -7x + 2x2 = 0

Solving
-6 + -7x + 2x2 = 0

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

Divide each side by '2'.
-3 + -3.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -3.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -3.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -3.5x + x2 = 0 + 3
-3.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-3.5x + x2 = 3

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 3 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 3 + 3.0625

Combine like terms: 3 + 3.0625 = 6.0625
3.0625 + -3.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.46221445 and -2.46221445.


Subproblem 1
x + -1.75 = 2.46221445

Simplifying
x + -1.75 = 2.46221445

Reorder the terms:
-1.75 + x = 2.46221445

Solving
-1.75 + x = 2.46221445

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.46221445 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.46221445 + 1.75
x = 2.46221445 + 1.75

Combine like terms: 2.46221445 + 1.75 = 4.21221445
x = 4.21221445

Simplifying
x = 4.21221445


Subproblem 2
x + -1.75 = -2.46221445

Simplifying
x + -1.75 = -2.46221445

Reorder the terms:
-1.75 + x = -2.46221445

Solving
-1.75 + x = -2.46221445

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.46221445 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.46221445 + 1.75
x = -2.46221445 + 1.75

Combine like terms: -2.46221445 + 1.75 = -0.71221445
x = -0.71221445

Simplifying
x = -0.71221445


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.21221445, -0.71221445}
Solution
x = {4.21221445, -0.71221445}

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