(3s+6)(2s-7)=0

Solution for (3s+6)(2s-7)=0 equation:

Simplifying
(3s + 6)(2s + -7) = 0

Reorder the terms:
(6 + 3s)(2s + -7) = 0

Reorder the terms:
(6 + 3s)(-7 + 2s) = 0

Multiply (6 + 3s) * (-7 + 2s)
(6(-7 + 2s) + 3s * (-7 + 2s)) = 0
((-7 * 6 + 2s * 6) + 3s * (-7 + 2s)) = 0
((-42 + 12s) + 3s * (-7 + 2s)) = 0
(-42 + 12s + (-7 * 3s + 2s * 3s)) = 0
(-42 + 12s + (-21s + 6s2)) = 0

Combine like terms: 12s + -21s = -9s
(-42 + -9s + 6s2) = 0

Solving
-42 + -9s + 6s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -3s + 2s2) = 0

Factor a trinomial.
3((-2 + -1s)(7 + -2s)) = 0

Ignore the factor 3.
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 '(7 + -2s)' equal to zero and attempt to solve:

Simplifying
7 + -2s = 0

Solving
7 + -2s = 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 + -2s = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2s = 0 + -7
-2s = 0 + -7

Combine like terms: 0 + -7 = -7
-2s = -7

Divide each side by '-2'.
s = 3.5

Simplifying
s = 3.5
Solution
s = {-2, 3.5}