q(10p-3q)=3p^2

Solution for q(10p-3q)=3p^2 equation:

Simplifying
q(10p + -3q) = 3p2
(10p * q + -3q * q) = 3p2
(10pq + -3q2) = 3p2

Solving
10pq + -3q2 = 3p2

Solving for variable 'p'.

Reorder the terms:
10pq + -3p2 + -3q2 = 3p2 + -3p2

Combine like terms: 3p2 + -3p2 = 0
10pq + -3p2 + -3q2 = 0

Factor a trinomial.
(-3p + q)(p + -3q) = 0

Subproblem 1
Set the factor '(-3p + q)' equal to zero and attempt to solve:

Simplifying
-3p + q = 0

Solving
-3p + q = 0

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

Add '-1q' to each side of the equation.
-3p + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
-3p + 0 = 0 + -1q
-3p = 0 + -1q
Remove the zero:
-3p = -1q

Divide each side by '-3'.
p = 0.3333333333q

Simplifying
p = 0.3333333333q
Subproblem 2
Set the factor '(p + -3q)' equal to zero and attempt to solve:

Simplifying
p + -3q = 0

Solving
p + -3q = 0

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

Add '3q' to each side of the equation.
p + -3q + 3q = 0 + 3q

Combine like terms: -3q + 3q = 0
p + 0 = 0 + 3q
p = 0 + 3q
Remove the zero:
p = 3q

Simplifying
p = 3q
Solution
p = {0.3333333333q, 3q}