2w^2-14w+24=0

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Solution for 2w^2-14w+24=0 equation:


Simplifying
2w2 + -14w + 24 = 0

Reorder the terms:
24 + -14w + 2w2 = 0

Solving
24 + -14w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -7w + w2) = 0

Factor a trinomial.
2((3 + -1w)(4 + -1w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3

Subproblem 2

Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4

Solution

w = {3, 4}

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