-6w^2+51w-105=0

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Solution for -6w^2+51w-105=0 equation:


Simplifying
-6w2 + 51w + -105 = 0

Reorder the terms:
-105 + 51w + -6w2 = 0

Solving
-105 + 51w + -6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 17w + -2w2) = 0

Factor a trinomial.
3((-5 + w)(7 + -2w)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 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 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 5

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 = {5, 3.5}

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