(s+2)(s-5)=30

Solution for (s+2)(s-5)=30 equation:

Simplifying
(s + 2)(s + -5) = 30

Reorder the terms:
(2 + s)(s + -5) = 30

Reorder the terms:
(2 + s)(-5 + s) = 30

Multiply (2 + s) * (-5 + s)
(2(-5 + s) + s(-5 + s)) = 30
((-5 * 2 + s * 2) + s(-5 + s)) = 30
((-10 + 2s) + s(-5 + s)) = 30
(-10 + 2s + (-5 * s + s * s)) = 30
(-10 + 2s + (-5s + s2)) = 30

Combine like terms: 2s + -5s = -3s
(-10 + -3s + s2) = 30

Solving
-10 + -3s + s2 = 30

Solving for variable 's'.

Reorder the terms:
-10 + -30 + -3s + s2 = 30 + -30

Combine like terms: -10 + -30 = -40
-40 + -3s + s2 = 30 + -30

Combine like terms: 30 + -30 = 0
-40 + -3s + s2 = 0

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

Subproblem 1
Set the factor '(-5 + -1s)' equal to zero and attempt to solve:

Simplifying
-5 + -1s = 0

Solving
-5 + -1s = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1s = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1s = 0 + 5
-1s = 0 + 5

Combine like terms: 0 + 5 = 5
-1s = 5

Divide each side by '-1'.
s = -5

Simplifying
s = -5
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 = {-5, 8}