4x^2=36x-72

Solution for 4x^2=36x-72 equation:

Simplifying
4x2 = 36x + -72

Reorder the terms:
4x2 = -72 + 36x

Solving
4x2 = -72 + 36x

Solving for variable 'x'.

Reorder the terms:
72 + -36x + 4x2 = -72 + 36x + 72 + -36x

Reorder the terms:
72 + -36x + 4x2 = -72 + 72 + 36x + -36x

Combine like terms: -72 + 72 = 0
72 + -36x + 4x2 = 0 + 36x + -36x
72 + -36x + 4x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
72 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -9x + x2) = 0

Factor a trinomial.
4((3 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {3, 6}