180=8x(7x+10)

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

Simplifying
180 = 8x(7x + 10)

Reorder the terms:
180 = 8x(10 + 7x)
180 = (10 * 8x + 7x * 8x)
180 = (80x + 56x2)

Solving
180 = 80x + 56x2

Solving for variable 'x'.

Reorder the terms:
180 + -80x + -56x2 = 80x + -80x + 56x2 + -56x2

Combine like terms: 80x + -80x = 0
180 + -80x + -56x2 = 0 + 56x2 + -56x2
180 + -80x + -56x2 = 56x2 + -56x2

Combine like terms: 56x2 + -56x2 = 0
180 + -80x + -56x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + -20x + -14x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(45 + -20x + -14x2)' equal to zero and attempt to solve:

Simplifying
45 + -20x + -14x2 = 0

Solving
45 + -20x + -14x2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-3.214285714 + 1.428571429x + x2 = 0

Move the constant term to the right:

Add '3.214285714' to each side of the equation.
-3.214285714 + 1.428571429x + 3.214285714 + x2 = 0 + 3.214285714

Reorder the terms:
-3.214285714 + 3.214285714 + 1.428571429x + x2 = 0 + 3.214285714

Combine like terms: -3.214285714 + 3.214285714 = 0.000000000
0.000000000 + 1.428571429x + x2 = 0 + 3.214285714
1.428571429x + x2 = 0 + 3.214285714

Combine like terms: 0 + 3.214285714 = 3.214285714
1.428571429x + x2 = 3.214285714

The x term is 1.428571429x.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429x + 0.5102040819 + x2 = 3.214285714 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429x + x2 = 3.214285714 + 0.5102040819

Combine like terms: 3.214285714 + 0.5102040819 = 3.7244897959
0.5102040819 + 1.428571429x + x2 = 3.7244897959

Factor a perfect square on the left side:
(x + 0.7142857145)(x + 0.7142857145) = 3.7244897959

Calculate the square root of the right side: 1.929893727

Break this problem into two subproblems by setting 
(x + 0.7142857145) equal to 1.929893727 and -1.929893727.

Subproblem 1
x + 0.7142857145 = 1.929893727

Simplifying
x + 0.7142857145 = 1.929893727

Reorder the terms:
0.7142857145 + x = 1.929893727

Solving
0.7142857145 + x = 1.929893727

Solving for variable 'x'.

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

Add '-0.7142857145' to each side of the equation.
0.7142857145 + -0.7142857145 + x = 1.929893727 + -0.7142857145

Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000
0.0000000000 + x = 1.929893727 + -0.7142857145
x = 1.929893727 + -0.7142857145

Combine like terms: 1.929893727 + -0.7142857145 = 1.2156080125
x = 1.2156080125

Simplifying
x = 1.2156080125

Subproblem 2
x + 0.7142857145 = -1.929893727

Simplifying
x + 0.7142857145 = -1.929893727

Reorder the terms:
0.7142857145 + x = -1.929893727

Solving
0.7142857145 + x = -1.929893727

Solving for variable 'x'.

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

Add '-0.7142857145' to each side of the equation.
0.7142857145 + -0.7142857145 + x = -1.929893727 + -0.7142857145

Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000
0.0000000000 + x = -1.929893727 + -0.7142857145
x = -1.929893727 + -0.7142857145

Combine like terms: -1.929893727 + -0.7142857145 = -2.6441794415
x = -2.6441794415

Simplifying
x = -2.6441794415

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2156080125, -2.6441794415}
Solution
x = {1.2156080125, -2.6441794415}