9n^2+30=47n+2n^2

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Solution for 9n^2+30=47n+2n^2 equation:


Simplifying
9n2 + 30 = 47n + 2n2

Reorder the terms:
30 + 9n2 = 47n + 2n2

Solving
30 + 9n2 = 47n + 2n2

Solving for variable 'n'.

Reorder the terms:
30 + -47n + 9n2 + -2n2 = 47n + 2n2 + -47n + -2n2

Combine like terms: 9n2 + -2n2 = 7n2
30 + -47n + 7n2 = 47n + 2n2 + -47n + -2n2

Reorder the terms:
30 + -47n + 7n2 = 47n + -47n + 2n2 + -2n2

Combine like terms: 47n + -47n = 0
30 + -47n + 7n2 = 0 + 2n2 + -2n2
30 + -47n + 7n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
30 + -47n + 7n2 = 0

Factor a trinomial.
(5 + -7n)(6 + -1n) = 0

Subproblem 1

Set the factor '(5 + -7n)' equal to zero and attempt to solve: Simplifying 5 + -7n = 0 Solving 5 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n = 0 + -5 -7n = 0 + -5 Combine like terms: 0 + -5 = -5 -7n = -5 Divide each side by '-7'. n = 0.7142857143 Simplifying n = 0.7142857143

Subproblem 2

Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6

Solution

n = {0.7142857143, 6}

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