4x^2+10x-6=180

Solution for 4x^2+10x-6=180 equation:

Simplifying
4x2 + 10x + -6 = 180

Reorder the terms:
-6 + 10x + 4x2 = 180

Solving
-6 + 10x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-6 + -180 + 10x + 4x2 = 180 + -180

Combine like terms: -6 + -180 = -186
-186 + 10x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-186 + 10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-93 + 5x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-93 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-93 + 5x + 2x2 = 0

Solving
-93 + 5x + 2x2 = 0

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

Divide each side by '2'.
-46.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '46.5' to each side of the equation.
-46.5 + 2.5x + 46.5 + x2 = 0 + 46.5

Reorder the terms:
-46.5 + 46.5 + 2.5x + x2 = 0 + 46.5

Combine like terms: -46.5 + 46.5 = 0.0
0.0 + 2.5x + x2 = 0 + 46.5
2.5x + x2 = 0 + 46.5

Combine like terms: 0 + 46.5 = 46.5
2.5x + x2 = 46.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 46.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 46.5 + 1.5625

Combine like terms: 46.5 + 1.5625 = 48.0625
1.5625 + 2.5x + x2 = 48.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 48.0625

Calculate the square root of the right side: 6.932712312

Break this problem into two subproblems by setting 
(x + 1.25) equal to 6.932712312 and -6.932712312.

Subproblem 1
x + 1.25 = 6.932712312

Simplifying
x + 1.25 = 6.932712312

Reorder the terms:
1.25 + x = 6.932712312

Solving
1.25 + x = 6.932712312

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 6.932712312 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 6.932712312 + -1.25
x = 6.932712312 + -1.25

Combine like terms: 6.932712312 + -1.25 = 5.682712312
x = 5.682712312

Simplifying
x = 5.682712312

Subproblem 2
x + 1.25 = -6.932712312

Simplifying
x + 1.25 = -6.932712312

Reorder the terms:
1.25 + x = -6.932712312

Solving
1.25 + x = -6.932712312

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -6.932712312 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -6.932712312 + -1.25
x = -6.932712312 + -1.25

Combine like terms: -6.932712312 + -1.25 = -8.182712312
x = -8.182712312

Simplifying
x = -8.182712312

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.682712312, -8.182712312}
Solution
x = {5.682712312, -8.182712312}