q^2+30q=-4q^2+10q+2400

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Solution for q^2+30q=-4q^2+10q+2400 equation: 


Simplifying
q2 + 30q = -4q2 + 10q + 2400

Reorder the terms:
30q + q2 = -4q2 + 10q + 2400

Reorder the terms:
30q + q2 = 2400 + 10q + -4q2

Solving
30q + q2 = 2400 + 10q + -4q2

Solving for variable 'q'.

Reorder the terms:
-2400 + 30q + -10q + q2 + 4q2 = 2400 + 10q + -4q2 + -2400 + -10q + 4q2

Combine like terms: 30q + -10q = 20q
-2400 + 20q + q2 + 4q2 = 2400 + 10q + -4q2 + -2400 + -10q + 4q2

Combine like terms: q2 + 4q2 = 5q2
-2400 + 20q + 5q2 = 2400 + 10q + -4q2 + -2400 + -10q + 4q2

Reorder the terms:
-2400 + 20q + 5q2 = 2400 + -2400 + 10q + -10q + -4q2 + 4q2

Combine like terms: 2400 + -2400 = 0
-2400 + 20q + 5q2 = 0 + 10q + -10q + -4q2 + 4q2
-2400 + 20q + 5q2 = 10q + -10q + -4q2 + 4q2

Combine like terms: 10q + -10q = 0
-2400 + 20q + 5q2 = 0 + -4q2 + 4q2
-2400 + 20q + 5q2 = -4q2 + 4q2

Combine like terms: -4q2 + 4q2 = 0
-2400 + 20q + 5q2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-480 + 4q + q2) = 0

Factor a trinomial.
5((-24 + -1q)(20 + -1q)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-24 + -1q)' equal to zero and attempt to solve:

Simplifying
-24 + -1q = 0

Solving
-24 + -1q = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1q = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1q = 0 + 24
-1q = 0 + 24

Combine like terms: 0 + 24 = 24
-1q = 24

Divide each side by '-1'.
q = -24

Simplifying
q = -24

Subproblem 2
Set the factor '(20 + -1q)' equal to zero and attempt to solve:

Simplifying
20 + -1q = 0

Solving
20 + -1q = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1q = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1q = 0 + -20
-1q = 0 + -20

Combine like terms: 0 + -20 = -20
-1q = -20

Divide each side by '-1'.
q = 20

Simplifying
q = 20
Solution
q = {-24, 20}

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