8q^2-4q=7q^2-8q+12

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Solution for 8q^2-4q=7q^2-8q+12 equation:


Simplifying
8q2 + -4q = 7q2 + -8q + 12

Reorder the terms:
-4q + 8q2 = 7q2 + -8q + 12

Reorder the terms:
-4q + 8q2 = 12 + -8q + 7q2

Solving
-4q + 8q2 = 12 + -8q + 7q2

Solving for variable 'q'.

Reorder the terms:
-12 + -4q + 8q + 8q2 + -7q2 = 12 + -8q + 7q2 + -12 + 8q + -7q2

Combine like terms: -4q + 8q = 4q
-12 + 4q + 8q2 + -7q2 = 12 + -8q + 7q2 + -12 + 8q + -7q2

Combine like terms: 8q2 + -7q2 = 1q2
-12 + 4q + 1q2 = 12 + -8q + 7q2 + -12 + 8q + -7q2

Reorder the terms:
-12 + 4q + 1q2 = 12 + -12 + -8q + 8q + 7q2 + -7q2

Combine like terms: 12 + -12 = 0
-12 + 4q + 1q2 = 0 + -8q + 8q + 7q2 + -7q2
-12 + 4q + 1q2 = -8q + 8q + 7q2 + -7q2

Combine like terms: -8q + 8q = 0
-12 + 4q + 1q2 = 0 + 7q2 + -7q2
-12 + 4q + 1q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-12 + 4q + 1q2 = 0

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

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 '(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 = {-6, 2}

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