8q^2-5q=7q^2-7q+24

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Solution for 8q^2-5q=7q^2-7q+24 equation:


Simplifying
8q2 + -5q = 7q2 + -7q + 24

Reorder the terms:
-5q + 8q2 = 7q2 + -7q + 24

Reorder the terms:
-5q + 8q2 = 24 + -7q + 7q2

Solving
-5q + 8q2 = 24 + -7q + 7q2

Solving for variable 'q'.

Reorder the terms:
-24 + -5q + 7q + 8q2 + -7q2 = 24 + -7q + 7q2 + -24 + 7q + -7q2

Combine like terms: -5q + 7q = 2q
-24 + 2q + 8q2 + -7q2 = 24 + -7q + 7q2 + -24 + 7q + -7q2

Combine like terms: 8q2 + -7q2 = 1q2
-24 + 2q + 1q2 = 24 + -7q + 7q2 + -24 + 7q + -7q2

Reorder the terms:
-24 + 2q + 1q2 = 24 + -24 + -7q + 7q + 7q2 + -7q2

Combine like terms: 24 + -24 = 0
-24 + 2q + 1q2 = 0 + -7q + 7q + 7q2 + -7q2
-24 + 2q + 1q2 = -7q + 7q + 7q2 + -7q2

Combine like terms: -7q + 7q = 0
-24 + 2q + 1q2 = 0 + 7q2 + -7q2
-24 + 2q + 1q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-24 + 2q + 1q2 = 0

Factor a trinomial.
(-6 + -1q)(4 + -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 '(4 + -1q)' equal to zero and attempt to solve: Simplifying 4 + -1q = 0 Solving 4 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1q = 0 + -4 -1q = 0 + -4 Combine like terms: 0 + -4 = -4 -1q = -4 Divide each side by '-1'. q = 4 Simplifying q = 4

Solution

q = {-6, 4}

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