(3r-5p)(3r+4p)=

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


Simplifying
(3r + -5p)(3r + 4p) = 0

Reorder the terms:
(-5p + 3r)(3r + 4p) = 0

Reorder the terms:
(-5p + 3r)(4p + 3r) = 0

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

Reorder the terms:
((-15pr + -20p2) + 3r * (4p + 3r)) = 0
((-15pr + -20p2) + 3r * (4p + 3r)) = 0
(-15pr + -20p2 + (4p * 3r + 3r * 3r)) = 0
(-15pr + -20p2 + (12pr + 9r2)) = 0

Reorder the terms:
(-15pr + 12pr + -20p2 + 9r2) = 0

Combine like terms: -15pr + 12pr = -3pr
(-3pr + -20p2 + 9r2) = 0

Solving
-3pr + -20p2 + 9r2 = 0

Solving for variable 'p'.

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


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

Simplifying
-4p + -3r = 0

Solving
-4p + -3r = 0

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

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

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

Divide each side by '-4'.
p = -0.75r

Simplifying
p = -0.75r

Subproblem 2
Set the factor '(5p + -3r)' equal to zero and attempt to solve:

Simplifying
5p + -3r = 0

Solving
5p + -3r = 0

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

Add '3r' to each side of the equation.
5p + -3r + 3r = 0 + 3r

Combine like terms: -3r + 3r = 0
5p + 0 = 0 + 3r
5p = 0 + 3r
Remove the zero:
5p = 3r

Divide each side by '5'.
p = 0.6r

Simplifying
p = 0.6r
Solution
p = {-0.75r, 0.6r}

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