(3w+2)w=40

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Solution for (3w+2)w=40 equation:


Simplifying
(3w + 2) * w = 40

Reorder the terms:
(2 + 3w) * w = 40

Reorder the terms for easier multiplication:
w(2 + 3w) = 40
(2 * w + 3w * w) = 40
(2w + 3w2) = 40

Solving
2w + 3w2 = 40

Solving for variable 'w'.

Reorder the terms:
-40 + 2w + 3w2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 2w + 3w2 = 0

Factor a trinomial.
(-4 + -1w)(10 + -3w) = 0

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 '(10 + -3w)' equal to zero and attempt to solve: Simplifying 10 + -3w = 0 Solving 10 + -3w = 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 + -3w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3w = 0 + -10 -3w = 0 + -10 Combine like terms: 0 + -10 = -10 -3w = -10 Divide each side by '-3'. w = 3.333333333 Simplifying w = 3.333333333

Solution

w = {-4, 3.333333333}

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