n^2+12n=-4n^2-7

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Solution for n^2+12n=-4n^2-7 equation:


Simplifying
n2 + 12n = -4n2 + -7

Reorder the terms:
12n + n2 = -4n2 + -7

Reorder the terms:
12n + n2 = -7 + -4n2

Solving
12n + n2 = -7 + -4n2

Solving for variable 'n'.

Reorder the terms:
7 + 12n + n2 + 4n2 = -7 + -4n2 + 7 + 4n2

Combine like terms: n2 + 4n2 = 5n2
7 + 12n + 5n2 = -7 + -4n2 + 7 + 4n2

Reorder the terms:
7 + 12n + 5n2 = -7 + 7 + -4n2 + 4n2

Combine like terms: -7 + 7 = 0
7 + 12n + 5n2 = 0 + -4n2 + 4n2
7 + 12n + 5n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 0
7 + 12n + 5n2 = 0

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

Subproblem 1

Set the factor '(7 + 5n)' equal to zero and attempt to solve: Simplifying 7 + 5n = 0 Solving 7 + 5n = 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 + 5n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5n = 0 + -7 5n = 0 + -7 Combine like terms: 0 + -7 = -7 5n = -7 Divide each side by '5'. n = -1.4 Simplifying n = -1.4

Subproblem 2

Set the factor '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 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 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Simplifying n = -1

Solution

n = {-1.4, -1}

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