6w^2-39w-45=0

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Solution for 6w^2-39w-45=0 equation:


Simplifying
6w2 + -39w + -45 = 0

Reorder the terms:
-45 + -39w + 6w2 = 0

Solving
-45 + -39w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -13w + 2w2) = 0

Factor a trinomial.
3((-1 + -1w)(15 + -2w)) = 0

Ignore the factor 3.

Subproblem 1

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

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 = {-1, 7.5}

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