(2w+5)*w=12

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Solution for (2w+5)*w=12 equation:


Simplifying
(2w + 5) * w = 12

Reorder the terms:
(5 + 2w) * w = 12

Reorder the terms for easier multiplication:
w(5 + 2w) = 12
(5 * w + 2w * w) = 12
(5w + 2w2) = 12

Solving
5w + 2w2 = 12

Solving for variable 'w'.

Reorder the terms:
-12 + 5w + 2w2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 5w + 2w2 = 0

Factor a trinomial.
(-4 + -1w)(3 + -2w) = 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 '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5

Solution

w = {-4, 1.5}

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