(8x-10)6x=(10x+10)

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Solution for (8x-10)6x=(10x+10) equation: 


Simplifying
(8x + -10) * 6x = (10x + 10)

Reorder the terms:
(-10 + 8x) * 6x = (10x + 10)

Reorder the terms for easier multiplication:
6x(-10 + 8x) = (10x + 10)
(-10 * 6x + 8x * 6x) = (10x + 10)
(-60x + 48x2) = (10x + 10)

Reorder the terms:
-60x + 48x2 = (10 + 10x)

Remove parenthesis around (10 + 10x)
-60x + 48x2 = 10 + 10x

Solving
-60x + 48x2 = 10 + 10x

Solving for variable 'x'.

Reorder the terms:
-10 + -60x + -10x + 48x2 = 10 + 10x + -10 + -10x

Combine like terms: -60x + -10x = -70x
-10 + -70x + 48x2 = 10 + 10x + -10 + -10x

Reorder the terms:
-10 + -70x + 48x2 = 10 + -10 + 10x + -10x

Combine like terms: 10 + -10 = 0
-10 + -70x + 48x2 = 0 + 10x + -10x
-10 + -70x + 48x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-10 + -70x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -35x + 24x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -35x + 24x2)' equal to zero and attempt to solve:

Simplifying
-5 + -35x + 24x2 = 0

Solving
-5 + -35x + 24x2 = 0

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

Divide each side by '24'.
-0.2083333333 + -1.458333333x + x2 = 0

Move the constant term to the right:

Add '0.2083333333' to each side of the equation.
-0.2083333333 + -1.458333333x + 0.2083333333 + x2 = 0 + 0.2083333333

Reorder the terms:
-0.2083333333 + 0.2083333333 + -1.458333333x + x2 = 0 + 0.2083333333

Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000
0.0000000000 + -1.458333333x + x2 = 0 + 0.2083333333
-1.458333333x + x2 = 0 + 0.2083333333

Combine like terms: 0 + 0.2083333333 = 0.2083333333
-1.458333333x + x2 = 0.2083333333

The x term is -1.458333333x.  Take half its coefficient (-0.7291666665).
Square it (0.5316840275) and add it to both sides.

Add '0.5316840275' to each side of the equation.
-1.458333333x + 0.5316840275 + x2 = 0.2083333333 + 0.5316840275

Reorder the terms:
0.5316840275 + -1.458333333x + x2 = 0.2083333333 + 0.5316840275

Combine like terms: 0.2083333333 + 0.5316840275 = 0.7400173608
0.5316840275 + -1.458333333x + x2 = 0.7400173608

Factor a perfect square on the left side:
(x + -0.7291666665)(x + -0.7291666665) = 0.7400173608

Calculate the square root of the right side: 0.860242617

Break this problem into two subproblems by setting 
(x + -0.7291666665) equal to 0.860242617 and -0.860242617.


Subproblem 1
x + -0.7291666665 = 0.860242617

Simplifying
x + -0.7291666665 = 0.860242617

Reorder the terms:
-0.7291666665 + x = 0.860242617

Solving
-0.7291666665 + x = 0.860242617

Solving for variable 'x'.

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

Add '0.7291666665' to each side of the equation.
-0.7291666665 + 0.7291666665 + x = 0.860242617 + 0.7291666665

Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000
0.0000000000 + x = 0.860242617 + 0.7291666665
x = 0.860242617 + 0.7291666665

Combine like terms: 0.860242617 + 0.7291666665 = 1.5894092835
x = 1.5894092835

Simplifying
x = 1.5894092835


Subproblem 2
x + -0.7291666665 = -0.860242617

Simplifying
x + -0.7291666665 = -0.860242617

Reorder the terms:
-0.7291666665 + x = -0.860242617

Solving
-0.7291666665 + x = -0.860242617

Solving for variable 'x'.

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

Add '0.7291666665' to each side of the equation.
-0.7291666665 + 0.7291666665 + x = -0.860242617 + 0.7291666665

Combine like terms: -0.7291666665 + 0.7291666665 = 0.0000000000
0.0000000000 + x = -0.860242617 + 0.7291666665
x = -0.860242617 + 0.7291666665

Combine like terms: -0.860242617 + 0.7291666665 = -0.1310759505
x = -0.1310759505

Simplifying
x = -0.1310759505


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5894092835, -0.1310759505}
Solution
x = {1.5894092835, -0.1310759505}

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