(7p+3q)(-4p+11q)=

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Solution for (7p+3q)(-4p+11q)= equation: 


Simplifying
(7p + 3q)(-4p + 11q) = 0

Multiply (7p + 3q) * (-4p + 11q)
(7p * (-4p + 11q) + 3q * (-4p + 11q)) = 0
((-4p * 7p + 11q * 7p) + 3q * (-4p + 11q)) = 0

Reorder the terms:
((77pq + -28p2) + 3q * (-4p + 11q)) = 0
((77pq + -28p2) + 3q * (-4p + 11q)) = 0
(77pq + -28p2 + (-4p * 3q + 11q * 3q)) = 0
(77pq + -28p2 + (-12pq + 33q2)) = 0

Reorder the terms:
(77pq + -12pq + -28p2 + 33q2) = 0

Combine like terms: 77pq + -12pq = 65pq
(65pq + -28p2 + 33q2) = 0

Solving
65pq + -28p2 + 33q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-7p + -3q)(4p + -11q) = 0


Subproblem 1
Set the factor '(-7p + -3q)' equal to zero and attempt to solve:

Simplifying
-7p + -3q = 0

Solving
-7p + -3q = 0

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

Add '3q' to each side of the equation.
-7p + -3q + 3q = 0 + 3q

Combine like terms: -3q + 3q = 0
-7p + 0 = 0 + 3q
-7p = 0 + 3q
Remove the zero:
-7p = 3q

Divide each side by '-7'.
p = -0.4285714286q

Simplifying
p = -0.4285714286q

Subproblem 2
Set the factor '(4p + -11q)' equal to zero and attempt to solve:

Simplifying
4p + -11q = 0

Solving
4p + -11q = 0

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

Add '11q' to each side of the equation.
4p + -11q + 11q = 0 + 11q

Combine like terms: -11q + 11q = 0
4p + 0 = 0 + 11q
4p = 0 + 11q
Remove the zero:
4p = 11q

Divide each side by '4'.
p = 2.75q

Simplifying
p = 2.75q
Solution
p = {-0.4285714286q, 2.75q}

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