q^2+20q=-4q^2+10q+8400

Solution for q^2+20q=-4q^2+10q+8400 equation:

Simplifying
q2 + 20q = -4q2 + 10q + 8400

Reorder the terms:
20q + q2 = -4q2 + 10q + 8400

Reorder the terms:
20q + q2 = 8400 + 10q + -4q2

Solving
20q + q2 = 8400 + 10q + -4q2

Solving for variable 'q'.

Reorder the terms:
-8400 + 20q + -10q + q2 + 4q2 = 8400 + 10q + -4q2 + -8400 + -10q + 4q2

Combine like terms: 20q + -10q = 10q
-8400 + 10q + q2 + 4q2 = 8400 + 10q + -4q2 + -8400 + -10q + 4q2

Combine like terms: q2 + 4q2 = 5q2
-8400 + 10q + 5q2 = 8400 + 10q + -4q2 + -8400 + -10q + 4q2

Reorder the terms:
-8400 + 10q + 5q2 = 8400 + -8400 + 10q + -10q + -4q2 + 4q2

Combine like terms: 8400 + -8400 = 0
-8400 + 10q + 5q2 = 0 + 10q + -10q + -4q2 + 4q2
-8400 + 10q + 5q2 = 10q + -10q + -4q2 + 4q2

Combine like terms: 10q + -10q = 0
-8400 + 10q + 5q2 = 0 + -4q2 + 4q2
-8400 + 10q + 5q2 = -4q2 + 4q2

Combine like terms: -4q2 + 4q2 = 0
-8400 + 10q + 5q2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1680 + 2q + q2) = 0

Factor a trinomial.
5((-42 + -1q)(40 + -1q)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-42 + -1q)' equal to zero and attempt to solve:

Simplifying
-42 + -1q = 0

Solving
-42 + -1q = 0

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

Add '42' to each side of the equation.
-42 + 42 + -1q = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -1q = 0 + 42
-1q = 0 + 42

Combine like terms: 0 + 42 = 42
-1q = 42

Divide each side by '-1'.
q = -42

Simplifying
q = -42
Subproblem 2
Set the factor '(40 + -1q)' equal to zero and attempt to solve:

Simplifying
40 + -1q = 0

Solving
40 + -1q = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1q = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1q = 0 + -40
-1q = 0 + -40

Combine like terms: 0 + -40 = -40
-1q = -40

Divide each side by '-1'.
q = 40

Simplifying
q = 40
Solution
q = {-42, 40}