(2w+8)(w)=2170

Solution for (2w+8)(w)=2170 equation:

Simplifying
(2w + 8)(w) = 2170

Reorder the terms:
(8 + 2w)(w) = 2170

Reorder the terms for easier multiplication:
w(8 + 2w) = 2170
(8 * w + 2w * w) = 2170
(8w + 2w2) = 2170

Solving
8w + 2w2 = 2170

Solving for variable 'w'.

Reorder the terms:
-2170 + 8w + 2w2 = 2170 + -2170

Combine like terms: 2170 + -2170 = 0
-2170 + 8w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1085 + 4w + w2) = 0

Factor a trinomial.
2((-35 + -1w)(31 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + -1w)' equal to zero and attempt to solve:

Simplifying
-35 + -1w = 0

Solving
-35 + -1w = 0

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

Add '35' to each side of the equation.
-35 + 35 + -1w = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -1w = 0 + 35
-1w = 0 + 35

Combine like terms: 0 + 35 = 35
-1w = 35

Divide each side by '-1'.
w = -35

Simplifying
w = -35
Subproblem 2
Set the factor '(31 + -1w)' equal to zero and attempt to solve:

Simplifying
31 + -1w = 0

Solving
31 + -1w = 0

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

Add '-31' to each side of the equation.
31 + -31 + -1w = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -1w = 0 + -31
-1w = 0 + -31

Combine like terms: 0 + -31 = -31
-1w = -31

Divide each side by '-1'.
w = 31

Simplifying
w = 31
Solution
w = {-35, 31}