8q^2-4q=7q^2-7q+40

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Solution for 8q^2-4q=7q^2-7q+40 equation:


Simplifying
8q2 + -4q = 7q2 + -7q + 40

Reorder the terms:
-4q + 8q2 = 7q2 + -7q + 40

Reorder the terms:
-4q + 8q2 = 40 + -7q + 7q2

Solving
-4q + 8q2 = 40 + -7q + 7q2

Solving for variable 'q'.

Reorder the terms:
-40 + -4q + 7q + 8q2 + -7q2 = 40 + -7q + 7q2 + -40 + 7q + -7q2

Combine like terms: -4q + 7q = 3q
-40 + 3q + 8q2 + -7q2 = 40 + -7q + 7q2 + -40 + 7q + -7q2

Combine like terms: 8q2 + -7q2 = 1q2
-40 + 3q + 1q2 = 40 + -7q + 7q2 + -40 + 7q + -7q2

Reorder the terms:
-40 + 3q + 1q2 = 40 + -40 + -7q + 7q + 7q2 + -7q2

Combine like terms: 40 + -40 = 0
-40 + 3q + 1q2 = 0 + -7q + 7q + 7q2 + -7q2
-40 + 3q + 1q2 = -7q + 7q + 7q2 + -7q2

Combine like terms: -7q + 7q = 0
-40 + 3q + 1q2 = 0 + 7q2 + -7q2
-40 + 3q + 1q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-40 + 3q + 1q2 = 0

Factor a trinomial.
(-8 + -1q)(5 + -1q) = 0

Subproblem 1

Set the factor '(-8 + -1q)' equal to zero and attempt to solve: Simplifying -8 + -1q = 0 Solving -8 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1q = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1q = 0 + 8 -1q = 0 + 8 Combine like terms: 0 + 8 = 8 -1q = 8 Divide each side by '-1'. q = -8 Simplifying q = -8

Subproblem 2

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

Solution

q = {-8, 5}

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