6n^2-55=-7n

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Solution for 6n^2-55=-7n equation:


Simplifying
6n2 + -55 = -7n

Reorder the terms:
-55 + 6n2 = -7n

Solving
-55 + 6n2 = -7n

Solving for variable 'n'.

Reorder the terms:
-55 + 7n + 6n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
-55 + 7n + 6n2 = 0

Factor a trinomial.
(-11 + -3n)(5 + -2n) = 0

Subproblem 1

Set the factor '(-11 + -3n)' equal to zero and attempt to solve: Simplifying -11 + -3n = 0 Solving -11 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -3n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3n = 0 + 11 -3n = 0 + 11 Combine like terms: 0 + 11 = 11 -3n = 11 Divide each side by '-3'. n = -3.666666667 Simplifying n = -3.666666667

Subproblem 2

Set the factor '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 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 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5

Solution

n = {-3.666666667, 2.5}

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