(5p+2q)(-4p+11q)=

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Solution for (5p+2q)(-4p+11q)= equation: 


Simplifying
(5p + 2q)(-4p + 11q) = 0

Multiply (5p + 2q) * (-4p + 11q)
(5p * (-4p + 11q) + 2q * (-4p + 11q)) = 0
((-4p * 5p + 11q * 5p) + 2q * (-4p + 11q)) = 0

Reorder the terms:
((55pq + -20p2) + 2q * (-4p + 11q)) = 0
((55pq + -20p2) + 2q * (-4p + 11q)) = 0
(55pq + -20p2 + (-4p * 2q + 11q * 2q)) = 0
(55pq + -20p2 + (-8pq + 22q2)) = 0

Reorder the terms:
(55pq + -8pq + -20p2 + 22q2) = 0

Combine like terms: 55pq + -8pq = 47pq
(47pq + -20p2 + 22q2) = 0

Solving
47pq + -20p2 + 22q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-5p + -2q)(4p + -11q) = 0


Subproblem 1
Set the factor '(-5p + -2q)' equal to zero and attempt to solve:

Simplifying
-5p + -2q = 0

Solving
-5p + -2q = 0

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

Add '2q' to each side of the equation.
-5p + -2q + 2q = 0 + 2q

Combine like terms: -2q + 2q = 0
-5p + 0 = 0 + 2q
-5p = 0 + 2q
Remove the zero:
-5p = 2q

Divide each side by '-5'.
p = -0.4q

Simplifying
p = -0.4q

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 = {-0.4q, 2.75q}

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