(6p+4q)(-2p+7q)=

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Solution for (6p+4q)(-2p+7q)= equation: 


Simplifying
(6p + 4q)(-2p + 7q) = 0

Multiply (6p + 4q) * (-2p + 7q)
(6p * (-2p + 7q) + 4q * (-2p + 7q)) = 0
((-2p * 6p + 7q * 6p) + 4q * (-2p + 7q)) = 0

Reorder the terms:
((42pq + -12p2) + 4q * (-2p + 7q)) = 0
((42pq + -12p2) + 4q * (-2p + 7q)) = 0
(42pq + -12p2 + (-2p * 4q + 7q * 4q)) = 0
(42pq + -12p2 + (-8pq + 28q2)) = 0

Reorder the terms:
(42pq + -8pq + -12p2 + 28q2) = 0

Combine like terms: 42pq + -8pq = 34pq
(34pq + -12p2 + 28q2) = 0

Solving
34pq + -12p2 + 28q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17pq + -6p2 + 14q2) = 0

Factor a trinomial.
2((-3p + -2q)(2p + -7q)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3p + -2q)' equal to zero and attempt to solve:

Simplifying
-3p + -2q = 0

Solving
-3p + -2q = 0

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

Add '2q' to each side of the equation.
-3p + -2q + 2q = 0 + 2q

Combine like terms: -2q + 2q = 0
-3p + 0 = 0 + 2q
-3p = 0 + 2q
Remove the zero:
-3p = 2q

Divide each side by '-3'.
p = -0.6666666667q

Simplifying
p = -0.6666666667q

Subproblem 2
Set the factor '(2p + -7q)' equal to zero and attempt to solve:

Simplifying
2p + -7q = 0

Solving
2p + -7q = 0

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

Add '7q' to each side of the equation.
2p + -7q + 7q = 0 + 7q

Combine like terms: -7q + 7q = 0
2p + 0 = 0 + 7q
2p = 0 + 7q
Remove the zero:
2p = 7q

Divide each side by '2'.
p = 3.5q

Simplifying
p = 3.5q
Solution
p = {-0.6666666667q, 3.5q}

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