(6p+6q)(-4p+12q)=

Solution for (6p+6q)(-4p+12q)= equation:

Simplifying
(6p + 6q)(-4p + 12q) = 0

Multiply (6p + 6q) * (-4p + 12q)
(6p * (-4p + 12q) + 6q * (-4p + 12q)) = 0
((-4p * 6p + 12q * 6p) + 6q * (-4p + 12q)) = 0

Reorder the terms:
((72pq + -24p2) + 6q * (-4p + 12q)) = 0
((72pq + -24p2) + 6q * (-4p + 12q)) = 0
(72pq + -24p2 + (-4p * 6q + 12q * 6q)) = 0
(72pq + -24p2 + (-24pq + 72q2)) = 0

Reorder the terms:
(72pq + -24pq + -24p2 + 72q2) = 0

Combine like terms: 72pq + -24pq = 48pq
(48pq + -24p2 + 72q2) = 0

Solving
48pq + -24p2 + 72q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '24'.
24(2pq + -1p2 + 3q2) = 0

Factor a trinomial.
24((-1p + -1q)(p + -3q)) = 0

Ignore the factor 24.
Subproblem 1
Set the factor '(-1p + -1q)' equal to zero and attempt to solve:

Simplifying
-1p + -1q = 0

Solving
-1p + -1q = 0

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

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

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

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

Simplifying
p = -1q
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 = {-1q, 3q}