6w^2-28w+32=0

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Solution for 6w^2-28w+32=0 equation:


Simplifying
6w2 + -28w + 32 = 0

Reorder the terms:
32 + -28w + 6w2 = 0

Solving
32 + -28w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -14w + 3w2) = 0

Factor a trinomial.
2((2 + -1w)(8 + -3w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2

Subproblem 2

Set the factor '(8 + -3w)' equal to zero and attempt to solve: Simplifying 8 + -3w = 0 Solving 8 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3w = 0 + -8 -3w = 0 + -8 Combine like terms: 0 + -8 = -8 -3w = -8 Divide each side by '-3'. w = 2.666666667 Simplifying w = 2.666666667

Solution

w = {2, 2.666666667}

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