(w+12)(w)(5)=140

Solution for (w+12)(w)(5)=140 equation:

Simplifying
(w + 12)(w)(5) = 140

Reorder the terms:
(12 + w)(w)(5) = 140

Reorder the terms for easier multiplication:
5w(12 + w) = 140
(12 * 5w + w * 5w) = 140
(60w + 5w2) = 140

Solving
60w + 5w2 = 140

Solving for variable 'w'.

Reorder the terms:
-140 + 60w + 5w2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + 60w + 5w2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + 12w + w2) = 0

Factor a trinomial.
5((-14 + -1w)(2 + -1w)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-14 + -1w)' equal to zero and attempt to solve:

Simplifying
-14 + -1w = 0

Solving
-14 + -1w = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1w = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1w = 0 + 14
-1w = 0 + 14

Combine like terms: 0 + 14 = 14
-1w = 14

Divide each side by '-1'.
w = -14

Simplifying
w = -14
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-14, 2}