3x^2=24x-36

Solution for 3x^2=24x-36 equation:

Simplifying
3x2 = 24x + -36

Reorder the terms:
3x2 = -36 + 24x

Solving
3x2 = -36 + 24x

Solving for variable 'x'.

Reorder the terms:
36 + -24x + 3x2 = -36 + 24x + 36 + -24x

Reorder the terms:
36 + -24x + 3x2 = -36 + 36 + 24x + -24x

Combine like terms: -36 + 36 = 0
36 + -24x + 3x2 = 0 + 24x + -24x
36 + -24x + 3x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
36 + -24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -8x + x2) = 0

Factor a trinomial.
3((2 + -1x)(6 + -1x)) = 0

Ignore the factor 3.
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 '(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 = {2, 6}