4q^2-2q=3q^2-8q+16

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Solution for 4q^2-2q=3q^2-8q+16 equation: 


Simplifying
4q2 + -2q = 3q2 + -8q + 16

Reorder the terms:
-2q + 4q2 = 3q2 + -8q + 16

Reorder the terms:
-2q + 4q2 = 16 + -8q + 3q2

Solving
-2q + 4q2 = 16 + -8q + 3q2

Solving for variable 'q'.

Reorder the terms:
-16 + -2q + 8q + 4q2 + -3q2 = 16 + -8q + 3q2 + -16 + 8q + -3q2

Combine like terms: -2q + 8q = 6q
-16 + 6q + 4q2 + -3q2 = 16 + -8q + 3q2 + -16 + 8q + -3q2

Combine like terms: 4q2 + -3q2 = 1q2
-16 + 6q + 1q2 = 16 + -8q + 3q2 + -16 + 8q + -3q2

Reorder the terms:
-16 + 6q + 1q2 = 16 + -16 + -8q + 8q + 3q2 + -3q2

Combine like terms: 16 + -16 = 0
-16 + 6q + 1q2 = 0 + -8q + 8q + 3q2 + -3q2
-16 + 6q + 1q2 = -8q + 8q + 3q2 + -3q2

Combine like terms: -8q + 8q = 0
-16 + 6q + 1q2 = 0 + 3q2 + -3q2
-16 + 6q + 1q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 0
-16 + 6q + 1q2 = 0

Factor a trinomial.
(-8 + -1q)(2 + -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 '(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 = {-8, 2}

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