4x^2-24x+180=144

Solution for 4x^2-24x+180=144 equation:

Simplifying
4x2 + -24x + 180 = 144

Reorder the terms:
180 + -24x + 4x2 = 144

Solving
180 + -24x + 4x2 = 144

Solving for variable 'x'.

Reorder the terms:
180 + -144 + -24x + 4x2 = 144 + -144

Combine like terms: 180 + -144 = 36
36 + -24x + 4x2 = 144 + -144

Combine like terms: 144 + -144 = 0
36 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -6x + x2) = 0

Factor a trinomial.
4((3 + -1x)(3 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}