4w^7+24w^6+56w^5=0

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Solution for 4w^7+24w^6+56w^5=0 equation:


Simplifying
4w7 + 24w6 + 56w5 = 0

Reorder the terms:
56w5 + 24w6 + 4w7 = 0

Solving
56w5 + 24w6 + 4w7 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w5'.
4w5(14 + 6w + w2) = 0

Ignore the factor 4.

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 '(14 + 6w + w2)' equal to zero and attempt to solve: Simplifying 14 + 6w + w2 = 0 Solving 14 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 6w + -14 + w2 = 0 + -14 Reorder the terms: 14 + -14 + 6w + w2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 6w + w2 = 0 + -14 6w + w2 = 0 + -14 Combine like terms: 0 + -14 = -14 6w + w2 = -14 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = -14 + 9 Reorder the terms: 9 + 6w + w2 = -14 + 9 Combine like terms: -14 + 9 = -5 9 + 6w + w2 = -5 Factor a perfect square on the left side: (w + 3)(w + 3) = -5 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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