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

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


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

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

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

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

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

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

Solving for variable 'r'.
Remove the zero:
-5rs + -25r2 + 12s2 = 5rs + 25r2 + -12s2 + -5rs + -25r2 + 12s2

Reorder the terms:
-5rs + -25r2 + 12s2 = 5rs + -5rs + 25r2 + -25r2 + -12s2 + 12s2

Combine like terms: 5rs + -5rs = 0
-5rs + -25r2 + 12s2 = 0 + 25r2 + -25r2 + -12s2 + 12s2
-5rs + -25r2 + 12s2 = 25r2 + -25r2 + -12s2 + 12s2

Combine like terms: 25r2 + -25r2 = 0
-5rs + -25r2 + 12s2 = 0 + -12s2 + 12s2
-5rs + -25r2 + 12s2 = -12s2 + 12s2

Combine like terms: -12s2 + 12s2 = 0
-5rs + -25r2 + 12s2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
r = {-0.8s, 0.6s}

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