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

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


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

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

Reorder the terms:
((20rs + 25r2) + -3s * (5r + 4s)) = 0
((20rs + 25r2) + -3s * (5r + 4s)) = 0
(20rs + 25r2 + (5r * -3s + 4s * -3s)) = 0
(20rs + 25r2 + (-15rs + -12s2)) = 0

Reorder the terms:
(20rs + -15rs + 25r2 + -12s2) = 0

Combine like terms: 20rs + -15rs = 5rs
(5rs + 25r2 + -12s2) = 0

Solving
5rs + 25r2 + -12s2 = 0

Solving for variable 'r'.

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


Subproblem 1
Set the factor '(5r + -3s)' equal to zero and attempt to solve:

Simplifying
5r + -3s = 0

Solving
5r + -3s = 0

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

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

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

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

Simplifying
r = 0.6s

Subproblem 2
Set the factor '(5r + 4s)' equal to zero and attempt to solve:

Simplifying
5r + 4s = 0

Solving
5r + 4s = 0

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

Add '-4s' to each side of the equation.
5r + 4s + -4s = 0 + -4s

Combine like terms: 4s + -4s = 0
5r + 0 = 0 + -4s
5r = 0 + -4s
Remove the zero:
5r = -4s

Divide each side by '5'.
r = -0.8s

Simplifying
r = -0.8s
Solution
r = {0.6s, -0.8s}

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