9n^2=33n-28

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Solution for 9n^2=33n-28 equation:


Simplifying
9n2 = 33n + -28

Reorder the terms:
9n2 = -28 + 33n

Solving
9n2 = -28 + 33n

Solving for variable 'n'.

Reorder the terms:
28 + -33n + 9n2 = -28 + 33n + 28 + -33n

Reorder the terms:
28 + -33n + 9n2 = -28 + 28 + 33n + -33n

Combine like terms: -28 + 28 = 0
28 + -33n + 9n2 = 0 + 33n + -33n
28 + -33n + 9n2 = 33n + -33n

Combine like terms: 33n + -33n = 0
28 + -33n + 9n2 = 0

Factor a trinomial.
(4 + -3n)(7 + -3n) = 0

Subproblem 1

Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333

Subproblem 2

Set the factor '(7 + -3n)' equal to zero and attempt to solve: Simplifying 7 + -3n = 0 Solving 7 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3n = 0 + -7 -3n = 0 + -7 Combine like terms: 0 + -7 = -7 -3n = -7 Divide each side by '-3'. n = 2.333333333 Simplifying n = 2.333333333

Solution

n = {1.333333333, 2.333333333}

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