2(w+5)(w-24)=0

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Solution for 2(w+5)(w-24)=0 equation: 


Simplifying
2(w + 5)(w + -24) = 0

Reorder the terms:
2(5 + w)(w + -24) = 0

Reorder the terms:
2(5 + w)(-24 + w) = 0

Multiply (5 + w) * (-24 + w)
2(5(-24 + w) + w(-24 + w)) = 0
2((-24 * 5 + w * 5) + w(-24 + w)) = 0
2((-120 + 5w) + w(-24 + w)) = 0
2(-120 + 5w + (-24 * w + w * w)) = 0
2(-120 + 5w + (-24w + w2)) = 0

Combine like terms: 5w + -24w = -19w
2(-120 + -19w + w2) = 0
(-120 * 2 + -19w * 2 + w2 * 2) = 0
(-240 + -38w + 2w2) = 0

Solving
-240 + -38w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + -19w + w2) = 0

Factor a trinomial.
2((-5 + -1w)(24 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve:

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
w = -5

Simplifying
w = -5

Subproblem 2
Set the factor '(24 + -1w)' equal to zero and attempt to solve:

Simplifying
24 + -1w = 0

Solving
24 + -1w = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1w = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1w = 0 + -24
-1w = 0 + -24

Combine like terms: 0 + -24 = -24
-1w = -24

Divide each side by '-1'.
w = 24

Simplifying
w = 24
Solution
w = {-5, 24}

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