(2w-6)*w=80

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Solution for (2w-6)*w=80 equation:


Simplifying
(2w + -6) * w = 80

Reorder the terms:
(-6 + 2w) * w = 80

Reorder the terms for easier multiplication:
w(-6 + 2w) = 80
(-6 * w + 2w * w) = 80
(-6w + 2w2) = 80

Solving
-6w + 2w2 = 80

Solving for variable 'w'.

Reorder the terms:
-80 + -6w + 2w2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + -6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -3w + w2) = 0

Factor a trinomial.
2((-5 + -1w)(8 + -1w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5

Subproblem 2

Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8

Solution

w = {-5, 8}

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