6q^2-3q=5q^2-5q+63

Solution for 6q^2-3q=5q^2-5q+63 equation:

Simplifying
6q2 + -3q = 5q2 + -5q + 63

Reorder the terms:
-3q + 6q2 = 5q2 + -5q + 63

Reorder the terms:
-3q + 6q2 = 63 + -5q + 5q2

Solving
-3q + 6q2 = 63 + -5q + 5q2

Solving for variable 'q'.

Reorder the terms:
-63 + -3q + 5q + 6q2 + -5q2 = 63 + -5q + 5q2 + -63 + 5q + -5q2

Combine like terms: -3q + 5q = 2q
-63 + 2q + 6q2 + -5q2 = 63 + -5q + 5q2 + -63 + 5q + -5q2

Combine like terms: 6q2 + -5q2 = 1q2
-63 + 2q + 1q2 = 63 + -5q + 5q2 + -63 + 5q + -5q2

Reorder the terms:
-63 + 2q + 1q2 = 63 + -63 + -5q + 5q + 5q2 + -5q2

Combine like terms: 63 + -63 = 0
-63 + 2q + 1q2 = 0 + -5q + 5q + 5q2 + -5q2
-63 + 2q + 1q2 = -5q + 5q + 5q2 + -5q2

Combine like terms: -5q + 5q = 0
-63 + 2q + 1q2 = 0 + 5q2 + -5q2
-63 + 2q + 1q2 = 5q2 + -5q2

Combine like terms: 5q2 + -5q2 = 0
-63 + 2q + 1q2 = 0

Factor a trinomial.
(-9 + -1q)(7 + -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 '(7 + -1q)' equal to zero and attempt to solve:

Simplifying
7 + -1q = 0

Solving
7 + -1q = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1q = 0 + -7
-1q = 0 + -7

Combine like terms: 0 + -7 = -7
-1q = -7

Divide each side by '-1'.
q = 7

Simplifying
q = 7
Solution
q = {-9, 7}