((2w)-3)(w)-90=0

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Solution for ((2w)-3)(w)-90=0 equation:


Simplifying
((2w) + -3)(w) + -90 = 0

Reorder the terms:
(-3 + (2w))(w) + -90 = 0

Reorder the terms for easier multiplication:
w(-3 + (2w)) + -90 = 0
(-3 * w + (2w) * w) + -90 = 0
(-3w + 2w2) + -90 = 0

Reorder the terms:
-90 + -3w + 2w2 = 0

Solving
-90 + -3w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + -1w)(15 + -2w) = 0

Subproblem 1

Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6

Subproblem 2

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

Solution

w = {-6, 7.5}

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