2w^6-21w^5+27w^4=0

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Solution for 2w^6-21w^5+27w^4=0 equation:


Simplifying
2w6 + -21w5 + 27w4 = 0

Reorder the terms:
27w4 + -21w5 + 2w6 = 0

Solving
27w4 + -21w5 + 2w6 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w4'.
w4(27 + -21w + 2w2) = 0

Factor a trinomial.
w4((3 + -2w)(9 + -1w)) = 0

Subproblem 1

Set the factor 'w4' equal to zero and attempt to solve: Simplifying w4 = 0 Solving w4 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5

Subproblem 3

Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9

Solution

w = {1.5, 9}

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