4w^7+14w^6+10w^5=0

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Solution for 4w^7+14w^6+10w^5=0 equation:


Simplifying
4w7 + 14w6 + 10w5 = 0

Reorder the terms:
10w5 + 14w6 + 4w7 = 0

Solving
10w5 + 14w6 + 4w7 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w5'.
2w5(5 + 7w + 2w2) = 0

Factor a trinomial.
2w5((5 + 2w)(1 + w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'w5' equal to zero and attempt to solve: Simplifying w5 = 0 Solving w5 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w5 = 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 '(5 + 2w)' equal to zero and attempt to solve: Simplifying 5 + 2w = 0 Solving 5 + 2w = 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 + 2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2w = 0 + -5 2w = 0 + -5 Combine like terms: 0 + -5 = -5 2w = -5 Divide each side by '2'. w = -2.5 Simplifying w = -2.5

Subproblem 3

Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1

Solution

w = {-2.5, -1}

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