3x(5x-6)+90=180

Solution for 3x(5x-6)+90=180 equation:

Simplifying
3x(5x + -6) + 90 = 180

Reorder the terms:
3x(-6 + 5x) + 90 = 180
(-6 * 3x + 5x * 3x) + 90 = 180
(-18x + 15x2) + 90 = 180

Reorder the terms:
90 + -18x + 15x2 = 180

Solving
90 + -18x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
90 + -180 + -18x + 15x2 = 180 + -180

Combine like terms: 90 + -180 = -90
-90 + -18x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-90 + -18x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + -6x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-30 + -6x + 5x2)' equal to zero and attempt to solve:

Simplifying
-30 + -6x + 5x2 = 0

Solving
-30 + -6x + 5x2 = 0

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

Divide each side by '5'.
-6 + -1.2x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -1.2x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -1.2x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1.2x + x2 = 0 + 6
-1.2x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1.2x + x2 = 6

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 6 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 6 + 0.36

Combine like terms: 6 + 0.36 = 6.36
0.36 + -1.2x + x2 = 6.36

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 6.36

Calculate the square root of the right side: 2.521904043

Break this problem into two subproblems by setting 
(x + -0.6) equal to 2.521904043 and -2.521904043.

Subproblem 1
x + -0.6 = 2.521904043

Simplifying
x + -0.6 = 2.521904043

Reorder the terms:
-0.6 + x = 2.521904043

Solving
-0.6 + x = 2.521904043

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = 2.521904043 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = 2.521904043 + 0.6
x = 2.521904043 + 0.6

Combine like terms: 2.521904043 + 0.6 = 3.121904043
x = 3.121904043

Simplifying
x = 3.121904043

Subproblem 2
x + -0.6 = -2.521904043

Simplifying
x + -0.6 = -2.521904043

Reorder the terms:
-0.6 + x = -2.521904043

Solving
-0.6 + x = -2.521904043

Solving for variable 'x'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + x = -2.521904043 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + x = -2.521904043 + 0.6
x = -2.521904043 + 0.6

Combine like terms: -2.521904043 + 0.6 = -1.921904043
x = -1.921904043

Simplifying
x = -1.921904043

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.121904043, -1.921904043}
Solution
x = {3.121904043, -1.921904043}