3q^2+11q-72=5q

Solution for 3q^2+11q-72=5q equation:

Simplifying
3q2 + 11q + -72 = 5q

Reorder the terms:
-72 + 11q + 3q2 = 5q

Solving
-72 + 11q + 3q2 = 5q

Solving for variable 'q'.

Reorder the terms:
-72 + 11q + -5q + 3q2 = 5q + -5q

Combine like terms: 11q + -5q = 6q
-72 + 6q + 3q2 = 5q + -5q

Combine like terms: 5q + -5q = 0
-72 + 6q + 3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 2q + q2) = 0

Factor a trinomial.
3((-6 + -1q)(4 + -1q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1q)' equal to zero and attempt to solve:

Simplifying
-6 + -1q = 0

Solving
-6 + -1q = 0

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

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

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

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

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

Simplifying
q = -6
Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

Simplifying
q = 4
Solution
q = {-6, 4}