(12p+7q)(-3p+12q)=

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Solution for (12p+7q)(-3p+12q)= equation: 


Simplifying
(12p + 7q)(-3p + 12q) = 0

Multiply (12p + 7q) * (-3p + 12q)
(12p * (-3p + 12q) + 7q * (-3p + 12q)) = 0
((-3p * 12p + 12q * 12p) + 7q * (-3p + 12q)) = 0

Reorder the terms:
((144pq + -36p2) + 7q * (-3p + 12q)) = 0
((144pq + -36p2) + 7q * (-3p + 12q)) = 0
(144pq + -36p2 + (-3p * 7q + 12q * 7q)) = 0
(144pq + -36p2 + (-21pq + 84q2)) = 0

Reorder the terms:
(144pq + -21pq + -36p2 + 84q2) = 0

Combine like terms: 144pq + -21pq = 123pq
(123pq + -36p2 + 84q2) = 0

Solving
123pq + -36p2 + 84q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(41pq + -12p2 + 28q2) = 0

Factor a trinomial.
3((-12p + -7q)(p + -4q)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-12p + -7q)' equal to zero and attempt to solve:

Simplifying
-12p + -7q = 0

Solving
-12p + -7q = 0

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

Add '7q' to each side of the equation.
-12p + -7q + 7q = 0 + 7q

Combine like terms: -7q + 7q = 0
-12p + 0 = 0 + 7q
-12p = 0 + 7q
Remove the zero:
-12p = 7q

Divide each side by '-12'.
p = -0.5833333333q

Simplifying
p = -0.5833333333q

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 = {-0.5833333333q, 4q}

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