10x(7x-7)=(8x+6)

Solution for 10x(7x-7)=(8x+6) equation:

Simplifying
10x(7x + -7) = (8x + 6)

Reorder the terms:
10x(-7 + 7x) = (8x + 6)
(-7 * 10x + 7x * 10x) = (8x + 6)
(-70x + 70x2) = (8x + 6)

Reorder the terms:
-70x + 70x2 = (6 + 8x)

Remove parenthesis around (6 + 8x)
-70x + 70x2 = 6 + 8x

Solving
-70x + 70x2 = 6 + 8x

Solving for variable 'x'.

Reorder the terms:
-6 + -70x + -8x + 70x2 = 6 + 8x + -6 + -8x

Combine like terms: -70x + -8x = -78x
-6 + -78x + 70x2 = 6 + 8x + -6 + -8x

Reorder the terms:
-6 + -78x + 70x2 = 6 + -6 + 8x + -8x

Combine like terms: 6 + -6 = 0
-6 + -78x + 70x2 = 0 + 8x + -8x
-6 + -78x + 70x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-6 + -78x + 70x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -39x + 35x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -39x + 35x2)' equal to zero and attempt to solve:

Simplifying
-3 + -39x + 35x2 = 0

Solving
-3 + -39x + 35x2 = 0

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

Divide each side by '35'.
-0.08571428571 + -1.114285714x + x2 = 0

Move the constant term to the right:

Add '0.08571428571' to each side of the equation.
-0.08571428571 + -1.114285714x + 0.08571428571 + x2 = 0 + 0.08571428571

Reorder the terms:
-0.08571428571 + 0.08571428571 + -1.114285714x + x2 = 0 + 0.08571428571

Combine like terms: -0.08571428571 + 0.08571428571 = 0.00000000000
0.00000000000 + -1.114285714x + x2 = 0 + 0.08571428571
-1.114285714x + x2 = 0 + 0.08571428571

Combine like terms: 0 + 0.08571428571 = 0.08571428571
-1.114285714x + x2 = 0.08571428571

The x term is -1.114285714x.  Take half its coefficient (-0.557142857).
Square it (0.3104081631) and add it to both sides.

Add '0.3104081631' to each side of the equation.
-1.114285714x + 0.3104081631 + x2 = 0.08571428571 + 0.3104081631

Reorder the terms:
0.3104081631 + -1.114285714x + x2 = 0.08571428571 + 0.3104081631

Combine like terms: 0.08571428571 + 0.3104081631 = 0.39612244881
0.3104081631 + -1.114285714x + x2 = 0.39612244881

Factor a perfect square on the left side:
(x + -0.557142857)(x + -0.557142857) = 0.39612244881

Calculate the square root of the right side: 0.629382593

Break this problem into two subproblems by setting 
(x + -0.557142857) equal to 0.629382593 and -0.629382593.

Subproblem 1
x + -0.557142857 = 0.629382593

Simplifying
x + -0.557142857 = 0.629382593

Reorder the terms:
-0.557142857 + x = 0.629382593

Solving
-0.557142857 + x = 0.629382593

Solving for variable 'x'.

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

Add '0.557142857' to each side of the equation.
-0.557142857 + 0.557142857 + x = 0.629382593 + 0.557142857

Combine like terms: -0.557142857 + 0.557142857 = 0.000000000
0.000000000 + x = 0.629382593 + 0.557142857
x = 0.629382593 + 0.557142857

Combine like terms: 0.629382593 + 0.557142857 = 1.18652545
x = 1.18652545

Simplifying
x = 1.18652545

Subproblem 2
x + -0.557142857 = -0.629382593

Simplifying
x + -0.557142857 = -0.629382593

Reorder the terms:
-0.557142857 + x = -0.629382593

Solving
-0.557142857 + x = -0.629382593

Solving for variable 'x'.

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

Add '0.557142857' to each side of the equation.
-0.557142857 + 0.557142857 + x = -0.629382593 + 0.557142857

Combine like terms: -0.557142857 + 0.557142857 = 0.000000000
0.000000000 + x = -0.629382593 + 0.557142857
x = -0.629382593 + 0.557142857

Combine like terms: -0.629382593 + 0.557142857 = -0.072239736
x = -0.072239736

Simplifying
x = -0.072239736

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.18652545, -0.072239736}
Solution
x = {1.18652545, -0.072239736}