(w+-2)(w+5)=18

Solution for (w+-2)(w+5)=18 equation:

Simplifying
(w + -2)(w + 5) = 18

Reorder the terms:
(-2 + w)(w + 5) = 18

Reorder the terms:
(-2 + w)(5 + w) = 18

Multiply (-2 + w) * (5 + w)
(-2(5 + w) + w(5 + w)) = 18
((5 * -2 + w * -2) + w(5 + w)) = 18
((-10 + -2w) + w(5 + w)) = 18
(-10 + -2w + (5 * w + w * w)) = 18
(-10 + -2w + (5w + w2)) = 18

Combine like terms: -2w + 5w = 3w
(-10 + 3w + w2) = 18

Solving
-10 + 3w + w2 = 18

Solving for variable 'w'.

Reorder the terms:
-10 + -18 + 3w + w2 = 18 + -18

Combine like terms: -10 + -18 = -28
-28 + 3w + w2 = 18 + -18

Combine like terms: 18 + -18 = 0
-28 + 3w + w2 = 0

Factor a trinomial.
(-7 + -1w)(4 + -1w) = 0

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

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-7, 4}