(3p-2q)(4p+5q)=

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Solution for (3p-2q)(4p+5q)= equation: 


Simplifying
(3p + -2q)(4p + 5q) = 0

Multiply (3p + -2q) * (4p + 5q)
(3p * (4p + 5q) + -2q * (4p + 5q)) = 0
((4p * 3p + 5q * 3p) + -2q * (4p + 5q)) = 0

Reorder the terms:
((15pq + 12p2) + -2q * (4p + 5q)) = 0
((15pq + 12p2) + -2q * (4p + 5q)) = 0
(15pq + 12p2 + (4p * -2q + 5q * -2q)) = 0
(15pq + 12p2 + (-8pq + -10q2)) = 0

Reorder the terms:
(15pq + -8pq + 12p2 + -10q2) = 0

Combine like terms: 15pq + -8pq = 7pq
(7pq + 12p2 + -10q2) = 0

Solving
7pq + 12p2 + -10q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(3p + -2q)(4p + 5q) = 0


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 '(4p + 5q)' equal to zero and attempt to solve:

Simplifying
4p + 5q = 0

Solving
4p + 5q = 0

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

Add '-5q' to each side of the equation.
4p + 5q + -5q = 0 + -5q

Combine like terms: 5q + -5q = 0
4p + 0 = 0 + -5q
4p = 0 + -5q
Remove the zero:
4p = -5q

Divide each side by '4'.
p = -1.25q

Simplifying
p = -1.25q
Solution
p = {0.6666666667q, -1.25q}

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