(2w-5)w=52

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Solution for (2w-5)w=52 equation:


Simplifying
(2w + -5) * w = 52

Reorder the terms:
(-5 + 2w) * w = 52

Reorder the terms for easier multiplication:
w(-5 + 2w) = 52
(-5 * w + 2w * w) = 52
(-5w + 2w2) = 52

Solving
-5w + 2w2 = 52

Solving for variable 'w'.

Reorder the terms:
-52 + -5w + 2w2 = 52 + -52

Combine like terms: 52 + -52 = 0
-52 + -5w + 2w2 = 0

Factor a trinomial.
(-4 + -1w)(13 + -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 '(13 + -2w)' equal to zero and attempt to solve: Simplifying 13 + -2w = 0 Solving 13 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2w = 0 + -13 -2w = 0 + -13 Combine like terms: 0 + -13 = -13 -2w = -13 Divide each side by '-2'. w = 6.5 Simplifying w = 6.5

Solution

w = {-4, 6.5}

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