3k^4-13k^3+10k^2=0

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Solution for 3k^4-13k^3+10k^2=0 equation:


Simplifying
3k4 + -13k3 + 10k2 = 0

Reorder the terms:
10k2 + -13k3 + 3k4 = 0

Solving
10k2 + -13k3 + 3k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k2'.
k2(10 + -13k + 3k2) = 0

Factor a trinomial.
k2((1 + -1k)(10 + -3k)) = 0

Subproblem 1

Set the factor 'k2' equal to zero and attempt to solve: Simplifying k2 = 0 Solving k2 = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k2 = 0 Take the square root of each side: k = {0}

Subproblem 2

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

Subproblem 3

Set the factor '(10 + -3k)' equal to zero and attempt to solve: Simplifying 10 + -3k = 0 Solving 10 + -3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3k = 0 + -10 -3k = 0 + -10 Combine like terms: 0 + -10 = -10 -3k = -10 Divide each side by '-3'. k = 3.333333333 Simplifying k = 3.333333333

Solution

k = {0, 1, 3.333333333}

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