4q^2-3q=3q^2-7q+32

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Solution for 4q^2-3q=3q^2-7q+32 equation: 


Simplifying
4q2 + -3q = 3q2 + -7q + 32

Reorder the terms:
-3q + 4q2 = 3q2 + -7q + 32

Reorder the terms:
-3q + 4q2 = 32 + -7q + 3q2

Solving
-3q + 4q2 = 32 + -7q + 3q2

Solving for variable 'q'.

Reorder the terms:
-32 + -3q + 7q + 4q2 + -3q2 = 32 + -7q + 3q2 + -32 + 7q + -3q2

Combine like terms: -3q + 7q = 4q
-32 + 4q + 4q2 + -3q2 = 32 + -7q + 3q2 + -32 + 7q + -3q2

Combine like terms: 4q2 + -3q2 = 1q2
-32 + 4q + 1q2 = 32 + -7q + 3q2 + -32 + 7q + -3q2

Reorder the terms:
-32 + 4q + 1q2 = 32 + -32 + -7q + 7q + 3q2 + -3q2

Combine like terms: 32 + -32 = 0
-32 + 4q + 1q2 = 0 + -7q + 7q + 3q2 + -3q2
-32 + 4q + 1q2 = -7q + 7q + 3q2 + -3q2

Combine like terms: -7q + 7q = 0
-32 + 4q + 1q2 = 0 + 3q2 + -3q2
-32 + 4q + 1q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 0
-32 + 4q + 1q2 = 0

Factor a trinomial.
(-8 + -1q)(4 + -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 '(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 = {-8, 4}

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