0=w^2-30w-400

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Solution for 0=w^2-30w-400 equation: 


Simplifying
0 = w2 + -30w + -400

Reorder the terms:
0 = -400 + -30w + w2

Solving
0 = -400 + -30w + w2

Solving for variable 'w'.

Combine like terms: 0 + 400 = 400
400 + 30w + -1w2 = -400 + -30w + w2 + 400 + 30w + -1w2

Reorder the terms:
400 + 30w + -1w2 = -400 + 400 + -30w + 30w + w2 + -1w2

Combine like terms: -400 + 400 = 0
400 + 30w + -1w2 = 0 + -30w + 30w + w2 + -1w2
400 + 30w + -1w2 = -30w + 30w + w2 + -1w2

Combine like terms: -30w + 30w = 0
400 + 30w + -1w2 = 0 + w2 + -1w2
400 + 30w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
400 + 30w + -1w2 = 0

Factor a trinomial.
(40 + -1w)(10 + w) = 0


Subproblem 1
Set the factor '(40 + -1w)' equal to zero and attempt to solve:

Simplifying
40 + -1w = 0

Solving
40 + -1w = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1w = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1w = 0 + -40
-1w = 0 + -40

Combine like terms: 0 + -40 = -40
-1w = -40

Divide each side by '-1'.
w = 40

Simplifying
w = 40

Subproblem 2
Set the factor '(10 + w)' equal to zero and attempt to solve:

Simplifying
10 + w = 0

Solving
10 + w = 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 + w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + w = 0 + -10
w = 0 + -10

Combine like terms: 0 + -10 = -10
w = -10

Simplifying
w = -10
Solution
w = {40, -10}

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