-8(3s-4r)(9s+r)=

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Solution for -8(3s-4r)(9s+r)= equation: 


Simplifying
-8(3s + -4r)(9s + r) = 0

Reorder the terms:
-8(-4r + 3s)(9s + r) = 0

Reorder the terms:
-8(-4r + 3s)(r + 9s) = 0

Multiply (-4r + 3s) * (r + 9s)
-8(-4r * (r + 9s) + 3s * (r + 9s)) = 0
-8((r * -4r + 9s * -4r) + 3s * (r + 9s)) = 0

Reorder the terms:
-8((-36rs + -4r2) + 3s * (r + 9s)) = 0
-8((-36rs + -4r2) + 3s * (r + 9s)) = 0
-8(-36rs + -4r2 + (r * 3s + 9s * 3s)) = 0
-8(-36rs + -4r2 + (3rs + 27s2)) = 0

Reorder the terms:
-8(-36rs + 3rs + -4r2 + 27s2) = 0

Combine like terms: -36rs + 3rs = -33rs
-8(-33rs + -4r2 + 27s2) = 0
(-33rs * -8 + -4r2 * -8 + 27s2 * -8) = 0
(264rs + 32r2 + -216s2) = 0

Solving
264rs + 32r2 + -216s2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8'.
8(33rs + 4r2 + -27s2) = 0

Factor a trinomial.
8((4r + -3s)(r + 9s)) = 0

Ignore the factor 8.

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

Simplifying
4r + -3s = 0

Solving
4r + -3s = 0

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

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

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

Divide each side by '4'.
r = 0.75s

Simplifying
r = 0.75s

Subproblem 2
Set the factor '(r + 9s)' equal to zero and attempt to solve:

Simplifying
r + 9s = 0

Solving
r + 9s = 0

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

Add '-9s' to each side of the equation.
r + 9s + -9s = 0 + -9s

Combine like terms: 9s + -9s = 0
r + 0 = 0 + -9s
r = 0 + -9s
Remove the zero:
r = -9s

Simplifying
r = -9s
Solution
r = {0.75s, -9s}

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