(8p+6q)(-3p+12q)=0

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Solution for (8p+6q)(-3p+12q)=0 equation:


Simplifying
(8p + 6q)(-3p + 12q) = 0

Multiply (8p + 6q) * (-3p + 12q)
(8p * (-3p + 12q) + 6q * (-3p + 12q)) = 0
((-3p * 8p + 12q * 8p) + 6q * (-3p + 12q)) = 0

Reorder the terms:
((96pq + -24p2) + 6q * (-3p + 12q)) = 0
((96pq + -24p2) + 6q * (-3p + 12q)) = 0
(96pq + -24p2 + (-3p * 6q + 12q * 6q)) = 0
(96pq + -24p2 + (-18pq + 72q2)) = 0

Reorder the terms:
(96pq + -18pq + -24p2 + 72q2) = 0

Combine like terms: 96pq + -18pq = 78pq
(78pq + -24p2 + 72q2) = 0

Solving
78pq + -24p2 + 72q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '6'.
6(13pq + -4p2 + 12q2) = 0

Factor a trinomial.
6((-4p + -3q)(p + -4q)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-4p + -3q)' equal to zero and attempt to solve: Simplifying -4p + -3q = 0 Solving -4p + -3q = 0 Move all terms containing p to the left, all other terms to the right. Add '3q' to each side of the equation. -4p + -3q + 3q = 0 + 3q Combine like terms: -3q + 3q = 0 -4p + 0 = 0 + 3q -4p = 0 + 3q Remove the zero: -4p = 3q Divide each side by '-4'. p = -0.75q Simplifying p = -0.75q

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 = {-0.75q, 4q}

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