(s-8)(5s+10)=0

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Solution for (s-8)(5s+10)=0 equation: 


Simplifying
(s + -8)(5s + 10) = 0

Reorder the terms:
(-8 + s)(5s + 10) = 0

Reorder the terms:
(-8 + s)(10 + 5s) = 0

Multiply (-8 + s) * (10 + 5s)
(-8(10 + 5s) + s(10 + 5s)) = 0
((10 * -8 + 5s * -8) + s(10 + 5s)) = 0
((-80 + -40s) + s(10 + 5s)) = 0
(-80 + -40s + (10 * s + 5s * s)) = 0
(-80 + -40s + (10s + 5s2)) = 0

Combine like terms: -40s + 10s = -30s
(-80 + -30s + 5s2) = 0

Solving
-80 + -30s + 5s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -6s + s2) = 0

Factor a trinomial.
5((-2 + -1s)(8 + -1s)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + -1s)' equal to zero and attempt to solve:

Simplifying
-2 + -1s = 0

Solving
-2 + -1s = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1s = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1s = 0 + 2
-1s = 0 + 2

Combine like terms: 0 + 2 = 2
-1s = 2

Divide each side by '-1'.
s = -2

Simplifying
s = -2

Subproblem 2
Set the factor '(8 + -1s)' equal to zero and attempt to solve:

Simplifying
8 + -1s = 0

Solving
8 + -1s = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1s = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1s = 0 + -8
-1s = 0 + -8

Combine like terms: 0 + -8 = -8
-1s = -8

Divide each side by '-1'.
s = 8

Simplifying
s = 8
Solution
s = {-2, 8}

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