(8x-10)7x=180

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Solution for (8x-10)7x=180 equation: 


Simplifying
(8x + -10) * 7x = 180

Reorder the terms:
(-10 + 8x) * 7x = 180

Reorder the terms for easier multiplication:
7x(-10 + 8x) = 180
(-10 * 7x + 8x * 7x) = 180
(-70x + 56x2) = 180

Solving
-70x + 56x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -70x + 56x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -70x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -35x + 28x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + -35x + 28x2)' equal to zero and attempt to solve:

Simplifying
-90 + -35x + 28x2 = 0

Solving
-90 + -35x + 28x2 = 0

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

Divide each side by '28'.
-3.214285714 + -1.25x + x2 = 0

Move the constant term to the right:

Add '3.214285714' to each side of the equation.
-3.214285714 + -1.25x + 3.214285714 + x2 = 0 + 3.214285714

Reorder the terms:
-3.214285714 + 3.214285714 + -1.25x + x2 = 0 + 3.214285714

Combine like terms: -3.214285714 + 3.214285714 = 0.000000000
0.000000000 + -1.25x + x2 = 0 + 3.214285714
-1.25x + x2 = 0 + 3.214285714

Combine like terms: 0 + 3.214285714 = 3.214285714
-1.25x + x2 = 3.214285714

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 3.214285714 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 3.214285714 + 0.390625

Combine like terms: 3.214285714 + 0.390625 = 3.604910714
0.390625 + -1.25x + x2 = 3.604910714

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 3.604910714

Calculate the square root of the right side: 1.898660242

Break this problem into two subproblems by setting 
(x + -0.625) equal to 1.898660242 and -1.898660242.


Subproblem 1
x + -0.625 = 1.898660242

Simplifying
x + -0.625 = 1.898660242

Reorder the terms:
-0.625 + x = 1.898660242

Solving
-0.625 + x = 1.898660242

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 1.898660242 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 1.898660242 + 0.625
x = 1.898660242 + 0.625

Combine like terms: 1.898660242 + 0.625 = 2.523660242
x = 2.523660242

Simplifying
x = 2.523660242


Subproblem 2
x + -0.625 = -1.898660242

Simplifying
x + -0.625 = -1.898660242

Reorder the terms:
-0.625 + x = -1.898660242

Solving
-0.625 + x = -1.898660242

Solving for variable 'x'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -1.898660242 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -1.898660242 + 0.625
x = -1.898660242 + 0.625

Combine like terms: -1.898660242 + 0.625 = -1.273660242
x = -1.273660242

Simplifying
x = -1.273660242


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.523660242, -1.273660242}
Solution
x = {2.523660242, -1.273660242}

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