(12s+7)(5s-15)=0

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Solution for (12s+7)(5s-15)=0 equation: 


Simplifying
(12s + 7)(5s + -15) = 0

Reorder the terms:
(7 + 12s)(5s + -15) = 0

Reorder the terms:
(7 + 12s)(-15 + 5s) = 0

Multiply (7 + 12s) * (-15 + 5s)
(7(-15 + 5s) + 12s * (-15 + 5s)) = 0
((-15 * 7 + 5s * 7) + 12s * (-15 + 5s)) = 0
((-105 + 35s) + 12s * (-15 + 5s)) = 0
(-105 + 35s + (-15 * 12s + 5s * 12s)) = 0
(-105 + 35s + (-180s + 60s2)) = 0

Combine like terms: 35s + -180s = -145s
(-105 + -145s + 60s2) = 0

Solving
-105 + -145s + 60s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29s + 12s2) = 0

Factor a trinomial.
5((-7 + -12s)(3 + -1s)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -12s)' equal to zero and attempt to solve:

Simplifying
-7 + -12s = 0

Solving
-7 + -12s = 0

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

Add '7' to each side of the equation.
-7 + 7 + -12s = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12s = 0 + 7
-12s = 0 + 7

Combine like terms: 0 + 7 = 7
-12s = 7

Divide each side by '-12'.
s = -0.5833333333

Simplifying
s = -0.5833333333

Subproblem 2
Set the factor '(3 + -1s)' equal to zero and attempt to solve:

Simplifying
3 + -1s = 0

Solving
3 + -1s = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1s = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1s = 0 + -3
-1s = 0 + -3

Combine like terms: 0 + -3 = -3
-1s = -3

Divide each side by '-1'.
s = 3

Simplifying
s = 3
Solution
s = {-0.5833333333, 3}

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