(2w-5)*w=150

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Solution for (2w-5)*w=150 equation:


Simplifying
(2w + -5) * w = 150

Reorder the terms:
(-5 + 2w) * w = 150

Reorder the terms for easier multiplication:
w(-5 + 2w) = 150
(-5 * w + 2w * w) = 150
(-5w + 2w2) = 150

Solving
-5w + 2w2 = 150

Solving for variable 'w'.

Reorder the terms:
-150 + -5w + 2w2 = 150 + -150

Combine like terms: 150 + -150 = 0
-150 + -5w + 2w2 = 0

Factor a trinomial.
(-15 + -2w)(10 + -1w) = 0

Subproblem 1

Set the factor '(-15 + -2w)' equal to zero and attempt to solve: Simplifying -15 + -2w = 0 Solving -15 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2w = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2w = 0 + 15 -2w = 0 + 15 Combine like terms: 0 + 15 = 15 -2w = 15 Divide each side by '-2'. w = -7.5 Simplifying w = -7.5

Subproblem 2

Set the factor '(10 + -1w)' equal to zero and attempt to solve: Simplifying 10 + -1w = 0 Solving 10 + -1w = 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 + -1w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1w = 0 + -10 -1w = 0 + -10 Combine like terms: 0 + -10 = -10 -1w = -10 Divide each side by '-1'. w = 10 Simplifying w = 10

Solution

w = {-7.5, 10}

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