4x^2-54x+180=88

Solution for 4x^2-54x+180=88 equation:

Simplifying
4x2 + -54x + 180 = 88

Reorder the terms:
180 + -54x + 4x2 = 88

Solving
180 + -54x + 4x2 = 88

Solving for variable 'x'.

Reorder the terms:
180 + -88 + -54x + 4x2 = 88 + -88

Combine like terms: 180 + -88 = 92
92 + -54x + 4x2 = 88 + -88

Combine like terms: 88 + -88 = 0
92 + -54x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(46 + -27x + 2x2) = 0

Factor a trinomial.
2((2 + -1x)(23 + -2x)) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(23 + -2x)' equal to zero and attempt to solve:

Simplifying
23 + -2x = 0

Solving
23 + -2x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -2x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -2x = 0 + -23
-2x = 0 + -23

Combine like terms: 0 + -23 = -23
-2x = -23

Divide each side by '-2'.
x = 11.5

Simplifying
x = 11.5
Solution
x = {2, 11.5}