(3p-4q)(p+q)=0

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Solution for (3p-4q)(p+q)=0 equation: 


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

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

Reorder the terms:
((3pq + 3p2) + -4q * (p + q)) = 0
((3pq + 3p2) + -4q * (p + q)) = 0
(3pq + 3p2 + (p * -4q + q * -4q)) = 0
(3pq + 3p2 + (-4pq + -4q2)) = 0

Reorder the terms:
(3pq + -4pq + 3p2 + -4q2) = 0

Combine like terms: 3pq + -4pq = -1pq
(-1pq + 3p2 + -4q2) = 0

Solving
-1pq + 3p2 + -4q2 = 0

Solving for variable 'p'.

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


Subproblem 1
Set the factor '(3p + -4q)' equal to zero and attempt to solve:

Simplifying
3p + -4q = 0

Solving
3p + -4q = 0

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

Add '4q' to each side of the equation.
3p + -4q + 4q = 0 + 4q

Combine like terms: -4q + 4q = 0
3p + 0 = 0 + 4q
3p = 0 + 4q
Remove the zero:
3p = 4q

Divide each side by '3'.
p = 1.333333333q

Simplifying
p = 1.333333333q

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

Simplifying
p + q = 0

Solving
p + q = 0

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

Add '-1q' to each side of the equation.
p + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
p + 0 = 0 + -1q
p = 0 + -1q
Remove the zero:
p = -1q

Simplifying
p = -1q
Solution
p = {1.333333333q, -1q}

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