14n^2+19n=-6

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Solution for 14n^2+19n=-6 equation:


Simplifying
14n2 + 19n = -6

Reorder the terms:
19n + 14n2 = -6

Solving
19n + 14n2 = -6

Solving for variable 'n'.

Reorder the terms:
6 + 19n + 14n2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 19n + 14n2 = 0

Factor a trinomial.
(6 + 7n)(1 + 2n) = 0

Subproblem 1

Set the factor '(6 + 7n)' equal to zero and attempt to solve: Simplifying 6 + 7n = 0 Solving 6 + 7n = 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 + 7n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7n = 0 + -6 7n = 0 + -6 Combine like terms: 0 + -6 = -6 7n = -6 Divide each side by '7'. n = -0.8571428571 Simplifying n = -0.8571428571

Subproblem 2

Set the factor '(1 + 2n)' equal to zero and attempt to solve: Simplifying 1 + 2n = 0 Solving 1 + 2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2n = 0 + -1 2n = 0 + -1 Combine like terms: 0 + -1 = -1 2n = -1 Divide each side by '2'. n = -0.5 Simplifying n = -0.5

Solution

n = {-0.8571428571, -0.5}

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