9w^7+24w^6+12w^5=0

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Solution for 9w^7+24w^6+12w^5=0 equation:


Simplifying
9w7 + 24w6 + 12w5 = 0

Reorder the terms:
12w5 + 24w6 + 9w7 = 0

Solving
12w5 + 24w6 + 9w7 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w5'.
3w5(4 + 8w + 3w2) = 0

Factor a trinomial.
3w5((2 + w)(2 + 3w)) = 0

Ignore the factor 3.

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 '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 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 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2

Subproblem 3

Set the factor '(2 + 3w)' equal to zero and attempt to solve: Simplifying 2 + 3w = 0 Solving 2 + 3w = 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 + 3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3w = 0 + -2 3w = 0 + -2 Combine like terms: 0 + -2 = -2 3w = -2 Divide each side by '3'. w = -0.6666666667 Simplifying w = -0.6666666667

Solution

w = {-2, -0.6666666667}

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