(5p+7q)(-2p+12q)=

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Solution for (5p+7q)(-2p+12q)= equation: 


Simplifying
(5p + 7q)(-2p + 12q) = 0

Multiply (5p + 7q) * (-2p + 12q)
(5p * (-2p + 12q) + 7q * (-2p + 12q)) = 0
((-2p * 5p + 12q * 5p) + 7q * (-2p + 12q)) = 0

Reorder the terms:
((60pq + -10p2) + 7q * (-2p + 12q)) = 0
((60pq + -10p2) + 7q * (-2p + 12q)) = 0
(60pq + -10p2 + (-2p * 7q + 12q * 7q)) = 0
(60pq + -10p2 + (-14pq + 84q2)) = 0

Reorder the terms:
(60pq + -14pq + -10p2 + 84q2) = 0

Combine like terms: 60pq + -14pq = 46pq
(46pq + -10p2 + 84q2) = 0

Solving
46pq + -10p2 + 84q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(23pq + -5p2 + 42q2) = 0

Factor a trinomial.
2((-5p + -7q)(p + -6q)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5p + -7q)' equal to zero and attempt to solve:

Simplifying
-5p + -7q = 0

Solving
-5p + -7q = 0

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

Add '7q' to each side of the equation.
-5p + -7q + 7q = 0 + 7q

Combine like terms: -7q + 7q = 0
-5p + 0 = 0 + 7q
-5p = 0 + 7q
Remove the zero:
-5p = 7q

Divide each side by '-5'.
p = -1.4q

Simplifying
p = -1.4q

Subproblem 2
Set the factor '(p + -6q)' equal to zero and attempt to solve:

Simplifying
p + -6q = 0

Solving
p + -6q = 0

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

Add '6q' to each side of the equation.
p + -6q + 6q = 0 + 6q

Combine like terms: -6q + 6q = 0
p + 0 = 0 + 6q
p = 0 + 6q
Remove the zero:
p = 6q

Simplifying
p = 6q
Solution
p = {-1.4q, 6q}

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