6q^2+4q=5q^2-3q+18

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Solution for 6q^2+4q=5q^2-3q+18 equation: 


Simplifying
6q2 + 4q = 5q2 + -3q + 18

Reorder the terms:
4q + 6q2 = 5q2 + -3q + 18

Reorder the terms:
4q + 6q2 = 18 + -3q + 5q2

Solving
4q + 6q2 = 18 + -3q + 5q2

Solving for variable 'q'.

Reorder the terms:
-18 + 4q + 3q + 6q2 + -5q2 = 18 + -3q + 5q2 + -18 + 3q + -5q2

Combine like terms: 4q + 3q = 7q
-18 + 7q + 6q2 + -5q2 = 18 + -3q + 5q2 + -18 + 3q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-18 + 7q + 1q2 = 18 + -3q + 5q2 + -18 + 3q + -5q2

Reorder the terms:
-18 + 7q + 1q2 = 18 + -18 + -3q + 3q + 5q2 + -5q2

Combine like terms: 18 + -18 = 0
-18 + 7q + 1q2 = 0 + -3q + 3q + 5q2 + -5q2
-18 + 7q + 1q2 = -3q + 3q + 5q2 + -5q2

Combine like terms: -3q + 3q = 0
-18 + 7q + 1q2 = 0 + 5q2 + -5q2
-18 + 7q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-18 + 7q + 1q2 = 0

Factor a trinomial.
(-9 + -1q)(2 + -1q) = 0


Subproblem 1
Set the factor '(-9 + -1q)' equal to zero and attempt to solve:

Simplifying
-9 + -1q = 0

Solving
-9 + -1q = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1q = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1q = 0 + 9
-1q = 0 + 9

Combine like terms: 0 + 9 = 9
-1q = 9

Divide each side by '-1'.
q = -9

Simplifying
q = -9

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 = {-9, 2}

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