-(4n+6)+8=-6(n+1)2n

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Solution for -(4n+6)+8=-6(n+1)2n equation:


Simplifying
-1(4n + 6) + 8 = -6(n + 1) * 2n

Reorder the terms:
-1(6 + 4n) + 8 = -6(n + 1) * 2n
(6 * -1 + 4n * -1) + 8 = -6(n + 1) * 2n
(-6 + -4n) + 8 = -6(n + 1) * 2n

Reorder the terms:
-6 + 8 + -4n = -6(n + 1) * 2n

Combine like terms: -6 + 8 = 2
2 + -4n = -6(n + 1) * 2n

Reorder the terms:
2 + -4n = -6(1 + n) * 2n

Reorder the terms for easier multiplication:
2 + -4n = -6 * 2n(1 + n)

Multiply -6 * 2
2 + -4n = -12n(1 + n)
2 + -4n = (1 * -12n + n * -12n)
2 + -4n = (-12n + -12n2)

Solving
2 + -4n = -12n + -12n2

Solving for variable 'n'.

Combine like terms: -4n + 12n = 8n
2 + 8n + 12n2 = -12n + -12n2 + 12n + 12n2

Reorder the terms:
2 + 8n + 12n2 = -12n + 12n + -12n2 + 12n2

Combine like terms: -12n + 12n = 0
2 + 8n + 12n2 = 0 + -12n2 + 12n2
2 + 8n + 12n2 = -12n2 + 12n2

Combine like terms: -12n2 + 12n2 = 0
2 + 8n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 4n + 6n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 4n + 6n2)' equal to zero and attempt to solve: Simplifying 1 + 4n + 6n2 = 0 Solving 1 + 4n + 6n2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 0.6666666667n + n2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.6666666667n + -0.1666666667 + n2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.6666666667n + n2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.6666666667n + n2 = 0 + -0.1666666667 0.6666666667n + n2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.6666666667n + n2 = -0.1666666667 The n term is 0.6666666667n. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667n + 0.1111111112 + n2 = -0.1666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667n + n2 = -0.1666666667 + 0.1111111112 Combine like terms: -0.1666666667 + 0.1111111112 = -0.0555555555 0.1111111112 + 0.6666666667n + n2 = -0.0555555555 Factor a perfect square on the left side: (n + 0.3333333334)(n + 0.3333333334) = -0.0555555555 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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