(6w+3)(w)=165

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Solution for (6w+3)(w)=165 equation:


Simplifying
(6w + 3)(w) = 165

Reorder the terms:
(3 + 6w)(w) = 165

Reorder the terms for easier multiplication:
w(3 + 6w) = 165
(3 * w + 6w * w) = 165
(3w + 6w2) = 165

Solving
3w + 6w2 = 165

Solving for variable 'w'.

Reorder the terms:
-165 + 3w + 6w2 = 165 + -165

Combine like terms: 165 + -165 = 0
-165 + 3w + 6w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-55 + w + 2w2) = 0

Factor a trinomial.
3((-11 + -2w)(5 + -1w)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-11 + -2w)' equal to zero and attempt to solve: Simplifying -11 + -2w = 0 Solving -11 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2w = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2w = 0 + 11 -2w = 0 + 11 Combine like terms: 0 + 11 = 11 -2w = 11 Divide each side by '-2'. w = -5.5 Simplifying w = -5.5

Subproblem 2

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

Solution

w = {-5.5, 5}

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