(2w+2)(w)=24

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Solution for (2w+2)(w)=24 equation:


Simplifying
(2w + 2)(w) = 24

Reorder the terms:
(2 + 2w)(w) = 24

Reorder the terms for easier multiplication:
w(2 + 2w) = 24
(2 * w + 2w * w) = 24
(2w + 2w2) = 24

Solving
2w + 2w2 = 24

Solving for variable 'w'.

Reorder the terms:
-24 + 2w + 2w2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 2w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + w + w2) = 0

Factor a trinomial.
2((-4 + -1w)(3 + -1w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + -1w)' equal to zero and attempt to solve: Simplifying -4 + -1w = 0 Solving -4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1w = 0 + 4 -1w = 0 + 4 Combine like terms: 0 + 4 = 4 -1w = 4 Divide each side by '-1'. w = -4 Simplifying w = -4

Subproblem 2

Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3

Solution

w = {-4, 3}

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