Q^2+5Q=6Q^3

Solution for Q^2+5Q=6Q^3 equation:

Simplifying
Q2 + 5Q = 6Q3

Reorder the terms:
5Q + Q2 = 6Q3

Solving
5Q + Q2 = 6Q3

Solving for variable 'Q'.

Combine like terms: 6Q3 + -6Q3 = 0
5Q + Q2 + -6Q3 = 0

Factor out the Greatest Common Factor (GCF), 'Q'.
Q(5 + Q + -6Q2) = 0

Factor a trinomial.
Q((1 + -1Q)(5 + 6Q)) = 0

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
Subproblem 3
Set the factor '(5 + 6Q)' equal to zero and attempt to solve:

Simplifying
5 + 6Q = 0

Solving
5 + 6Q = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6Q = 0 + -5

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

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

Divide each side by '6'.
Q = -0.8333333333

Simplifying
Q = -0.8333333333
Solution
Q = {0, 1, -0.8333333333}