3q^2+57=-60q

Solution for 3q^2+57=-60q equation:

Simplifying
3q2 + 57 = -60q

Reorder the terms:
57 + 3q2 = -60q

Solving
57 + 3q2 = -60q

Solving for variable 'q'.

Reorder the terms:
57 + 60q + 3q2 = -60q + 60q

Combine like terms: -60q + 60q = 0
57 + 60q + 3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(19 + 20q + q2) = 0

Factor a trinomial.
3((19 + q)(1 + q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(19 + q)' equal to zero and attempt to solve:

Simplifying
19 + q = 0

Solving
19 + q = 0

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

Add '-19' to each side of the equation.
19 + -19 + q = 0 + -19

Combine like terms: 19 + -19 = 0
0 + q = 0 + -19
q = 0 + -19

Combine like terms: 0 + -19 = -19
q = -19

Simplifying
q = -19
Subproblem 2
Set the factor '(1 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

Solving
1 + q = 0

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

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

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

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

Simplifying
q = -1
Solution
q = {-19, -1}