(2w-1)w=21

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Solution for (2w-1)w=21 equation:


Simplifying
(2w + -1) * w = 21

Reorder the terms:
(-1 + 2w) * w = 21

Reorder the terms for easier multiplication:
w(-1 + 2w) = 21
(-1 * w + 2w * w) = 21
(-1w + 2w2) = 21

Solving
-1w + 2w2 = 21

Solving for variable 'w'.

Reorder the terms:
-21 + -1w + 2w2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -1w + 2w2 = 0

Factor a trinomial.
(-3 + -1w)(7 + -2w) = 0

Subproblem 1

Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 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 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3

Subproblem 2

Set the factor '(7 + -2w)' equal to zero and attempt to solve: Simplifying 7 + -2w = 0 Solving 7 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2w = 0 + -7 -2w = 0 + -7 Combine like terms: 0 + -7 = -7 -2w = -7 Divide each side by '-2'. w = 3.5 Simplifying w = 3.5

Solution

w = {-3, 3.5}

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