q^2+8q-12=5q-2

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Solution for q^2+8q-12=5q-2 equation: 


Simplifying
q2 + 8q + -12 = 5q + -2

Reorder the terms:
-12 + 8q + q2 = 5q + -2

Reorder the terms:
-12 + 8q + q2 = -2 + 5q

Solving
-12 + 8q + q2 = -2 + 5q

Solving for variable 'q'.

Reorder the terms:
-12 + 2 + 8q + -5q + q2 = -2 + 5q + 2 + -5q

Combine like terms: -12 + 2 = -10
-10 + 8q + -5q + q2 = -2 + 5q + 2 + -5q

Combine like terms: 8q + -5q = 3q
-10 + 3q + q2 = -2 + 5q + 2 + -5q

Reorder the terms:
-10 + 3q + q2 = -2 + 2 + 5q + -5q

Combine like terms: -2 + 2 = 0
-10 + 3q + q2 = 0 + 5q + -5q
-10 + 3q + q2 = 5q + -5q

Combine like terms: 5q + -5q = 0
-10 + 3q + q2 = 0

Factor a trinomial.
(-5 + -1q)(2 + -1q) = 0


Subproblem 1
Set the factor '(-5 + -1q)' equal to zero and attempt to solve:

Simplifying
-5 + -1q = 0

Solving
-5 + -1q = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1q = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1q = 0 + 5
-1q = 0 + 5

Combine like terms: 0 + 5 = 5
-1q = 5

Divide each side by '-1'.
q = -5

Simplifying
q = -5

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

Simplifying
2 + -1q = 0

Solving
2 + -1q = 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 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Solution
q = {-5, 2}

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