(w)(w)+40w=384

Solution for (w)(w)+40w=384 equation:

Simplifying
(w)(w) + 40w = 384

Multiply w * w
w2 + 40w = 384

Reorder the terms:
40w + w2 = 384

Solving
40w + w2 = 384

Solving for variable 'w'.

Reorder the terms:
-384 + 40w + w2 = 384 + -384

Combine like terms: 384 + -384 = 0
-384 + 40w + w2 = 0

Factor a trinomial.
(-48 + -1w)(8 + -1w) = 0

Subproblem 1
Set the factor '(-48 + -1w)' equal to zero and attempt to solve:

Simplifying
-48 + -1w = 0

Solving
-48 + -1w = 0

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

Add '48' to each side of the equation.
-48 + 48 + -1w = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -1w = 0 + 48
-1w = 0 + 48

Combine like terms: 0 + 48 = 48
-1w = 48

Divide each side by '-1'.
w = -48

Simplifying
w = -48
Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8

Combine like terms: 0 + -8 = -8
-1w = -8

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Solution
w = {-48, 8}