9n^2=12n-4

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Solution for 9n^2=12n-4 equation:


Simplifying
9n2 = 12n + -4

Reorder the terms:
9n2 = -4 + 12n

Solving
9n2 = -4 + 12n

Solving for variable 'n'.

Reorder the terms:
4 + -12n + 9n2 = -4 + 12n + 4 + -12n

Reorder the terms:
4 + -12n + 9n2 = -4 + 4 + 12n + -12n

Combine like terms: -4 + 4 = 0
4 + -12n + 9n2 = 0 + 12n + -12n
4 + -12n + 9n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
4 + -12n + 9n2 = 0

Factor a trinomial.
(2 + -3n)(2 + -3n) = 0

Subproblem 1

Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667

Subproblem 2

Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667

Solution

n = {0.6666666667, 0.6666666667}

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