7n^4+66n^3+80n^2=0

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Solution for 7n^4+66n^3+80n^2=0 equation:


Simplifying
7n4 + 66n3 + 80n2 = 0

Reorder the terms:
80n2 + 66n3 + 7n4 = 0

Solving
80n2 + 66n3 + 7n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(80 + 66n + 7n2) = 0

Factor a trinomial.
n2((8 + n)(10 + 7n)) = 0

Subproblem 1

Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}

Subproblem 2

Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8

Subproblem 3

Set the factor '(10 + 7n)' equal to zero and attempt to solve: Simplifying 10 + 7n = 0 Solving 10 + 7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 7n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 7n = 0 + -10 7n = 0 + -10 Combine like terms: 0 + -10 = -10 7n = -10 Divide each side by '7'. n = -1.428571429 Simplifying n = -1.428571429

Solution

n = {0, -8, -1.428571429}

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