72x^2-180x+108=0

Solution for 72x^2-180x+108=0 equation:

Simplifying
72x2 + -180x + 108 = 0

Reorder the terms:
108 + -180x + 72x2 = 0

Solving
108 + -180x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '36'.
36(3 + -5x + 2x2) = 0

Factor a trinomial.
36((1 + -1x)(3 + -2x)) = 0

Ignore the factor 36.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1, 1.5}