6q^2-3q=5q^2-6q+28

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Solution for 6q^2-3q=5q^2-6q+28 equation: 


Simplifying
6q2 + -3q = 5q2 + -6q + 28

Reorder the terms:
-3q + 6q2 = 5q2 + -6q + 28

Reorder the terms:
-3q + 6q2 = 28 + -6q + 5q2

Solving
-3q + 6q2 = 28 + -6q + 5q2

Solving for variable 'q'.

Reorder the terms:
-28 + -3q + 6q + 6q2 + -5q2 = 28 + -6q + 5q2 + -28 + 6q + -5q2

Combine like terms: -3q + 6q = 3q
-28 + 3q + 6q2 + -5q2 = 28 + -6q + 5q2 + -28 + 6q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-28 + 3q + 1q2 = 28 + -6q + 5q2 + -28 + 6q + -5q2

Reorder the terms:
-28 + 3q + 1q2 = 28 + -28 + -6q + 6q + 5q2 + -5q2

Combine like terms: 28 + -28 = 0
-28 + 3q + 1q2 = 0 + -6q + 6q + 5q2 + -5q2
-28 + 3q + 1q2 = -6q + 6q + 5q2 + -5q2

Combine like terms: -6q + 6q = 0
-28 + 3q + 1q2 = 0 + 5q2 + -5q2
-28 + 3q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-28 + 3q + 1q2 = 0

Factor a trinomial.
(-7 + -1q)(4 + -1q) = 0


Subproblem 1
Set the factor '(-7 + -1q)' equal to zero and attempt to solve:

Simplifying
-7 + -1q = 0

Solving
-7 + -1q = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1q = 0 + 7
-1q = 0 + 7

Combine like terms: 0 + 7 = 7
-1q = 7

Divide each side by '-1'.
q = -7

Simplifying
q = -7

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 = {-7, 4}

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