(12p+5q)(-3p+12q)=

Solution for (12p+5q)(-3p+12q)= equation:

Simplifying
(12p + 5q)(-3p + 12q) = 0

Multiply (12p + 5q) * (-3p + 12q)
(12p * (-3p + 12q) + 5q * (-3p + 12q)) = 0
((-3p * 12p + 12q * 12p) + 5q * (-3p + 12q)) = 0

Reorder the terms:
((144pq + -36p2) + 5q * (-3p + 12q)) = 0
((144pq + -36p2) + 5q * (-3p + 12q)) = 0
(144pq + -36p2 + (-3p * 5q + 12q * 5q)) = 0
(144pq + -36p2 + (-15pq + 60q2)) = 0

Reorder the terms:
(144pq + -15pq + -36p2 + 60q2) = 0

Combine like terms: 144pq + -15pq = 129pq
(129pq + -36p2 + 60q2) = 0

Solving
129pq + -36p2 + 60q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(43pq + -12p2 + 20q2) = 0

Factor a trinomial.
3((-12p + -5q)(p + -4q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-12p + -5q)' equal to zero and attempt to solve:

Simplifying
-12p + -5q = 0

Solving
-12p + -5q = 0

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

Add '5q' to each side of the equation.
-12p + -5q + 5q = 0 + 5q

Combine like terms: -5q + 5q = 0
-12p + 0 = 0 + 5q
-12p = 0 + 5q
Remove the zero:
-12p = 5q

Divide each side by '-12'.
p = -0.4166666667q

Simplifying
p = -0.4166666667q
Subproblem 2
Set the factor '(p + -4q)' equal to zero and attempt to solve:

Simplifying
p + -4q = 0

Solving
p + -4q = 0

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

Add '4q' to each side of the equation.
p + -4q + 4q = 0 + 4q

Combine like terms: -4q + 4q = 0
p + 0 = 0 + 4q
p = 0 + 4q
Remove the zero:
p = 4q

Simplifying
p = 4q
Solution
p = {-0.4166666667q, 4q}