8q^2-5q=7q^2-8q+10

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Solution for 8q^2-5q=7q^2-8q+10 equation: 


Simplifying
8q2 + -5q = 7q2 + -8q + 10

Reorder the terms:
-5q + 8q2 = 7q2 + -8q + 10

Reorder the terms:
-5q + 8q2 = 10 + -8q + 7q2

Solving
-5q + 8q2 = 10 + -8q + 7q2

Solving for variable 'q'.

Reorder the terms:
-10 + -5q + 8q + 8q2 + -7q2 = 10 + -8q + 7q2 + -10 + 8q + -7q2

Combine like terms: -5q + 8q = 3q
-10 + 3q + 8q2 + -7q2 = 10 + -8q + 7q2 + -10 + 8q + -7q2

Combine like terms: 8q2 + -7q2 = 1q2
-10 + 3q + 1q2 = 10 + -8q + 7q2 + -10 + 8q + -7q2

Reorder the terms:
-10 + 3q + 1q2 = 10 + -10 + -8q + 8q + 7q2 + -7q2

Combine like terms: 10 + -10 = 0
-10 + 3q + 1q2 = 0 + -8q + 8q + 7q2 + -7q2
-10 + 3q + 1q2 = -8q + 8q + 7q2 + -7q2

Combine like terms: -8q + 8q = 0
-10 + 3q + 1q2 = 0 + 7q2 + -7q2
-10 + 3q + 1q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-10 + 3q + 1q2 = 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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