2w(w+15)=500

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Solution for 2w(w+15)=500 equation: 


Simplifying
2w(w + 15) = 500

Reorder the terms:
2w(15 + w) = 500
(15 * 2w + w * 2w) = 500
(30w + 2w2) = 500

Solving
30w + 2w2 = 500

Solving for variable 'w'.

Reorder the terms:
-500 + 30w + 2w2 = 500 + -500

Combine like terms: 500 + -500 = 0
-500 + 30w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-250 + 15w + w2) = 0

Factor a trinomial.
2((-25 + -1w)(10 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + -1w)' equal to zero and attempt to solve:

Simplifying
-25 + -1w = 0

Solving
-25 + -1w = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1w = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1w = 0 + 25
-1w = 0 + 25

Combine like terms: 0 + 25 = 25
-1w = 25

Divide each side by '-1'.
w = -25

Simplifying
w = -25

Subproblem 2
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
Solution
w = {-25, 10}

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