4n+6-2n=2n(n+3)

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Solution for 4n+6-2n=2n(n+3) equation:


Simplifying
4n + 6 + -2n = 2n(n + 3)

Reorder the terms:
6 + 4n + -2n = 2n(n + 3)

Combine like terms: 4n + -2n = 2n
6 + 2n = 2n(n + 3)

Reorder the terms:
6 + 2n = 2n(3 + n)
6 + 2n = (3 * 2n + n * 2n)
6 + 2n = (6n + 2n2)

Solving
6 + 2n = 6n + 2n2

Solving for variable 'n'.

Combine like terms: 2n + -6n = -4n
6 + -4n + -2n2 = 6n + 2n2 + -6n + -2n2

Reorder the terms:
6 + -4n + -2n2 = 6n + -6n + 2n2 + -2n2

Combine like terms: 6n + -6n = 0
6 + -4n + -2n2 = 0 + 2n2 + -2n2
6 + -4n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
6 + -4n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2n + -1n2) = 0

Factor a trinomial.
2((1 + -1n)(3 + n)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

n = {1, -3}

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