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

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


Simplifying
(4r + -1p)(5r + 3p) = 0

Reorder the terms:
(-1p + 4r)(5r + 3p) = 0

Reorder the terms:
(-1p + 4r)(3p + 5r) = 0

Multiply (-1p + 4r) * (3p + 5r)
(-1p * (3p + 5r) + 4r * (3p + 5r)) = 0
((3p * -1p + 5r * -1p) + 4r * (3p + 5r)) = 0

Reorder the terms:
((-5pr + -3p2) + 4r * (3p + 5r)) = 0
((-5pr + -3p2) + 4r * (3p + 5r)) = 0
(-5pr + -3p2 + (3p * 4r + 5r * 4r)) = 0
(-5pr + -3p2 + (12pr + 20r2)) = 0

Reorder the terms:
(-5pr + 12pr + -3p2 + 20r2) = 0

Combine like terms: -5pr + 12pr = 7pr
(7pr + -3p2 + 20r2) = 0

Solving
7pr + -3p2 + 20r2 = 0

Solving for variable 'p'.

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

Subproblem 1

Set the factor '(-3p + -5r)' equal to zero and attempt to solve: Simplifying -3p + -5r = 0 Solving -3p + -5r = 0 Move all terms containing p to the left, all other terms to the right. Add '5r' to each side of the equation. -3p + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 -3p + 0 = 0 + 5r -3p = 0 + 5r Remove the zero: -3p = 5r Divide each side by '-3'. p = -1.666666667r Simplifying p = -1.666666667r

Subproblem 2

Set the factor '(p + -4r)' equal to zero and attempt to solve: Simplifying p + -4r = 0 Solving p + -4r = 0 Move all terms containing p to the left, all other terms to the right. Add '4r' to each side of the equation. p + -4r + 4r = 0 + 4r Combine like terms: -4r + 4r = 0 p + 0 = 0 + 4r p = 0 + 4r Remove the zero: p = 4r Simplifying p = 4r

Solution

p = {-1.666666667r, 4r}

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