3x^2=15x+72

Solution for 3x^2=15x+72 equation:

Simplifying
3x2 = 15x + 72

Reorder the terms:
3x2 = 72 + 15x

Solving
3x2 = 72 + 15x

Solving for variable 'x'.

Reorder the terms:
-72 + -15x + 3x2 = 72 + 15x + -72 + -15x

Reorder the terms:
-72 + -15x + 3x2 = 72 + -72 + 15x + -15x

Combine like terms: 72 + -72 = 0
-72 + -15x + 3x2 = 0 + 15x + -15x
-72 + -15x + 3x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-72 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -5x + x2) = 0

Factor a trinomial.
3((-3 + -1x)(8 + -1x)) = 0

Ignore the factor 3.
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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}