72=3x^2-24x+117

Solution for 72=3x^2-24x+117 equation:

Simplifying
72 = 3x2 + -24x + 117

Reorder the terms:
72 = 117 + -24x + 3x2

Solving
72 = 117 + -24x + 3x2

Solving for variable 'x'.

Combine like terms: 72 + -117 = -45
-45 + 24x + -3x2 = 117 + -24x + 3x2 + -117 + 24x + -3x2

Reorder the terms:
-45 + 24x + -3x2 = 117 + -117 + -24x + 24x + 3x2 + -3x2

Combine like terms: 117 + -117 = 0
-45 + 24x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2
-45 + 24x + -3x2 = -24x + 24x + 3x2 + -3x2

Combine like terms: -24x + 24x = 0
-45 + 24x + -3x2 = 0 + 3x2 + -3x2
-45 + 24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-45 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 8x + -1x2) = 0

Factor a trinomial.
3((-5 + x)(3 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
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 = {5, 3}