8q^2+2q=7q^2-3q+24

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Solution for 8q^2+2q=7q^2-3q+24 equation: 


Simplifying
8q2 + 2q = 7q2 + -3q + 24

Reorder the terms:
2q + 8q2 = 7q2 + -3q + 24

Reorder the terms:
2q + 8q2 = 24 + -3q + 7q2

Solving
2q + 8q2 = 24 + -3q + 7q2

Solving for variable 'q'.

Reorder the terms:
-24 + 2q + 3q + 8q2 + -7q2 = 24 + -3q + 7q2 + -24 + 3q + -7q2

Combine like terms: 2q + 3q = 5q
-24 + 5q + 8q2 + -7q2 = 24 + -3q + 7q2 + -24 + 3q + -7q2

Combine like terms: 8q2 + -7q2 = 1q2
-24 + 5q + 1q2 = 24 + -3q + 7q2 + -24 + 3q + -7q2

Reorder the terms:
-24 + 5q + 1q2 = 24 + -24 + -3q + 3q + 7q2 + -7q2

Combine like terms: 24 + -24 = 0
-24 + 5q + 1q2 = 0 + -3q + 3q + 7q2 + -7q2
-24 + 5q + 1q2 = -3q + 3q + 7q2 + -7q2

Combine like terms: -3q + 3q = 0
-24 + 5q + 1q2 = 0 + 7q2 + -7q2
-24 + 5q + 1q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-24 + 5q + 1q2 = 0

Factor a trinomial.
(-8 + -1q)(3 + -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 '(3 + -1q)' equal to zero and attempt to solve:

Simplifying
3 + -1q = 0

Solving
3 + -1q = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

Simplifying
q = 3
Solution
q = {-8, 3}

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