5q^2+18q-8=8q-8

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Solution for 5q^2+18q-8=8q-8 equation: 


Simplifying
5q2 + 18q + -8 = 8q + -8

Reorder the terms:
-8 + 18q + 5q2 = 8q + -8

Reorder the terms:
-8 + 18q + 5q2 = -8 + 8q

Add '8' to each side of the equation.
-8 + 18q + 8 + 5q2 = -8 + 8 + 8q

Reorder the terms:
-8 + 8 + 18q + 5q2 = -8 + 8 + 8q

Combine like terms: -8 + 8 = 0
0 + 18q + 5q2 = -8 + 8 + 8q
18q + 5q2 = -8 + 8 + 8q

Combine like terms: -8 + 8 = 0
18q + 5q2 = 0 + 8q
18q + 5q2 = 8q

Solving
18q + 5q2 = 8q

Solving for variable 'q'.

Reorder the terms:
18q + -8q + 5q2 = 8q + -8q

Combine like terms: 18q + -8q = 10q
10q + 5q2 = 8q + -8q

Combine like terms: 8q + -8q = 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}

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