(w+5)(w-2)=60

Solution for (w+5)(w-2)=60 equation:

Simplifying
(w + 5)(w + -2) = 60

Reorder the terms:
(5 + w)(w + -2) = 60

Reorder the terms:
(5 + w)(-2 + w) = 60

Multiply (5 + w) * (-2 + w)
(5(-2 + w) + w(-2 + w)) = 60
((-2 * 5 + w * 5) + w(-2 + w)) = 60
((-10 + 5w) + w(-2 + w)) = 60
(-10 + 5w + (-2 * w + w * w)) = 60
(-10 + 5w + (-2w + w2)) = 60

Combine like terms: 5w + -2w = 3w
(-10 + 3w + w2) = 60

Solving
-10 + 3w + w2 = 60

Solving for variable 'w'.

Reorder the terms:
-10 + -60 + 3w + w2 = 60 + -60

Combine like terms: -10 + -60 = -70
-70 + 3w + w2 = 60 + -60

Combine like terms: 60 + -60 = 0
-70 + 3w + w2 = 0

Factor a trinomial.
(-10 + -1w)(7 + -1w) = 0

Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve:

Simplifying
-10 + -1w = 0

Solving
-10 + -1w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1w = 0 + 10
-1w = 0 + 10

Combine like terms: 0 + 10 = 10
-1w = 10

Divide each side by '-1'.
w = -10

Simplifying
w = -10
Subproblem 2
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
Solution
w = {-10, 7}