5q^2+16q-6=6q-6

Solution for 5q^2+16q-6=6q-6 equation:

Simplifying
5q2 + 16q + -6 = 6q + -6

Reorder the terms:
-6 + 16q + 5q2 = 6q + -6

Reorder the terms:
-6 + 16q + 5q2 = -6 + 6q

Add '6' to each side of the equation.
-6 + 16q + 6 + 5q2 = -6 + 6 + 6q

Reorder the terms:
-6 + 6 + 16q + 5q2 = -6 + 6 + 6q

Combine like terms: -6 + 6 = 0
0 + 16q + 5q2 = -6 + 6 + 6q
16q + 5q2 = -6 + 6 + 6q

Combine like terms: -6 + 6 = 0
16q + 5q2 = 0 + 6q
16q + 5q2 = 6q

Solving
16q + 5q2 = 6q

Solving for variable 'q'.

Reorder the terms:
16q + -6q + 5q2 = 6q + -6q

Combine like terms: 16q + -6q = 10q
10q + 5q2 = 6q + -6q

Combine like terms: 6q + -6q = 0
10q + 5q2 = 0

Factor out the Greatest Common Factor (GCF), '5q'.
5q(2 + q) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(2 + q)' equal to zero and attempt to solve:

Simplifying
2 + q = 0

Solving
2 + q = 0

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

Add '-2' to each side of the equation.
2 + -2 + q = 0 + -2

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

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

Simplifying
q = -2
Solution
q = {0, -2}