2(w+6)(w-4)=832

Solution for 2(w+6)(w-4)=832 equation:

Simplifying
2(w + 6)(w + -4) = 832

Reorder the terms:
2(6 + w)(w + -4) = 832

Reorder the terms:
2(6 + w)(-4 + w) = 832

Multiply (6 + w) * (-4 + w)
2(6(-4 + w) + w(-4 + w)) = 832
2((-4 * 6 + w * 6) + w(-4 + w)) = 832
2((-24 + 6w) + w(-4 + w)) = 832
2(-24 + 6w + (-4 * w + w * w)) = 832
2(-24 + 6w + (-4w + w2)) = 832

Combine like terms: 6w + -4w = 2w
2(-24 + 2w + w2) = 832
(-24 * 2 + 2w * 2 + w2 * 2) = 832
(-48 + 4w + 2w2) = 832

Solving
-48 + 4w + 2w2 = 832

Solving for variable 'w'.

Reorder the terms:
-48 + -832 + 4w + 2w2 = 832 + -832

Combine like terms: -48 + -832 = -880
-880 + 4w + 2w2 = 832 + -832

Combine like terms: 832 + -832 = 0
-880 + 4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-440 + 2w + w2) = 0

Factor a trinomial.
2((-22 + -1w)(20 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-22 + -1w)' equal to zero and attempt to solve:

Simplifying
-22 + -1w = 0

Solving
-22 + -1w = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1w = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1w = 0 + 22
-1w = 0 + 22

Combine like terms: 0 + 22 = 22
-1w = 22

Divide each side by '-1'.
w = -22

Simplifying
w = -22
Subproblem 2
Set the factor '(20 + -1w)' equal to zero and attempt to solve:

Simplifying
20 + -1w = 0

Solving
20 + -1w = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1w = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1w = 0 + -20
-1w = 0 + -20

Combine like terms: 0 + -20 = -20
-1w = -20

Divide each side by '-1'.
w = 20

Simplifying
w = 20
Solution
w = {-22, 20}