q^2+200=-10q+3200

Solution for q^2+200=-10q+3200 equation:

Simplifying
q2 + 200 = -10q + 3200

Reorder the terms:
200 + q2 = -10q + 3200

Reorder the terms:
200 + q2 = 3200 + -10q

Solving
200 + q2 = 3200 + -10q

Solving for variable 'q'.

Reorder the terms:
200 + -3200 + 10q + q2 = 3200 + -10q + -3200 + 10q

Combine like terms: 200 + -3200 = -3000
-3000 + 10q + q2 = 3200 + -10q + -3200 + 10q

Reorder the terms:
-3000 + 10q + q2 = 3200 + -3200 + -10q + 10q

Combine like terms: 3200 + -3200 = 0
-3000 + 10q + q2 = 0 + -10q + 10q
-3000 + 10q + q2 = -10q + 10q

Combine like terms: -10q + 10q = 0
-3000 + 10q + q2 = 0

Factor a trinomial.
(-60 + -1q)(50 + -1q) = 0

Subproblem 1
Set the factor '(-60 + -1q)' equal to zero and attempt to solve:

Simplifying
-60 + -1q = 0

Solving
-60 + -1q = 0

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

Add '60' to each side of the equation.
-60 + 60 + -1q = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -1q = 0 + 60
-1q = 0 + 60

Combine like terms: 0 + 60 = 60
-1q = 60

Divide each side by '-1'.
q = -60

Simplifying
q = -60
Subproblem 2
Set the factor '(50 + -1q)' equal to zero and attempt to solve:

Simplifying
50 + -1q = 0

Solving
50 + -1q = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1q = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1q = 0 + -50
-1q = 0 + -50

Combine like terms: 0 + -50 = -50
-1q = -50

Divide each side by '-1'.
q = 50

Simplifying
q = 50
Solution
q = {-60, 50}