w(2+3w)=16

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Solution for w(2+3w)=16 equation:


Simplifying
w(2 + 3w) = 16
(2 * w + 3w * w) = 16
(2w + 3w2) = 16

Solving
2w + 3w2 = 16

Solving for variable 'w'.

Reorder the terms:
-16 + 2w + 3w2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 2w + 3w2 = 0

Factor a trinomial.
(-8 + -3w)(2 + -1w) = 0

Subproblem 1

Set the factor '(-8 + -3w)' equal to zero and attempt to solve: Simplifying -8 + -3w = 0 Solving -8 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3w = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3w = 0 + 8 -3w = 0 + 8 Combine like terms: 0 + 8 = 8 -3w = 8 Divide each side by '-3'. w = -2.666666667 Simplifying w = -2.666666667

Subproblem 2

Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2

Solution

w = {-2.666666667, 2}

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