Q^2+5Q=6Q^2

Solution for Q^2+5Q=6Q^2 equation:

Simplifying
Q2 + 5Q = 6Q2

Reorder the terms:
5Q + Q2 = 6Q2

Solving
5Q + Q2 = 6Q2

Solving for variable 'Q'.

Combine like terms: Q2 + -6Q2 = -5Q2
5Q + -5Q2 = 6Q2 + -6Q2

Combine like terms: 6Q2 + -6Q2 = 0
5Q + -5Q2 = 0

Factor out the Greatest Common Factor (GCF), '5Q'.
5Q(1 + -1Q) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'Q' equal to zero and attempt to solve:

Simplifying
Q = 0

Solving
Q = 0

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

Simplifying
Q = 0
Subproblem 2
Set the factor '(1 + -1Q)' equal to zero and attempt to solve:

Simplifying
1 + -1Q = 0

Solving
1 + -1Q = 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 + -1Q = 0 + -1

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

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

Divide each side by '-1'.
Q = 1

Simplifying
Q = 1
Solution
Q = {0, 1}