4q^2-5q=3q^2-8q+40

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Solution for 4q^2-5q=3q^2-8q+40 equation: 


Simplifying
4q2 + -5q = 3q2 + -8q + 40

Reorder the terms:
-5q + 4q2 = 3q2 + -8q + 40

Reorder the terms:
-5q + 4q2 = 40 + -8q + 3q2

Solving
-5q + 4q2 = 40 + -8q + 3q2

Solving for variable 'q'.

Reorder the terms:
-40 + -5q + 8q + 4q2 + -3q2 = 40 + -8q + 3q2 + -40 + 8q + -3q2

Combine like terms: -5q + 8q = 3q
-40 + 3q + 4q2 + -3q2 = 40 + -8q + 3q2 + -40 + 8q + -3q2

Combine like terms: 4q2 + -3q2 = 1q2
-40 + 3q + 1q2 = 40 + -8q + 3q2 + -40 + 8q + -3q2

Reorder the terms:
-40 + 3q + 1q2 = 40 + -40 + -8q + 8q + 3q2 + -3q2

Combine like terms: 40 + -40 = 0
-40 + 3q + 1q2 = 0 + -8q + 8q + 3q2 + -3q2
-40 + 3q + 1q2 = -8q + 8q + 3q2 + -3q2

Combine like terms: -8q + 8q = 0
-40 + 3q + 1q2 = 0 + 3q2 + -3q2
-40 + 3q + 1q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 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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