24x+72=6x^2

Solution for 24x+72=6x^2 equation:

Simplifying
24x + 72 = 6x2

Reorder the terms:
72 + 24x = 6x2

Solving
72 + 24x = 6x2

Solving for variable 'x'.

Combine like terms: 6x2 + -6x2 = 0
72 + 24x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + 4x + -1x2) = 0

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {6, -2}