n(2n+3)-6=2n^2-5(n+6)

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Solution for n(2n+3)-6=2n^2-5(n+6) equation:


Simplifying
n(2n + 3) + -6 = 2n2 + -5(n + 6)

Reorder the terms:
n(3 + 2n) + -6 = 2n2 + -5(n + 6)
(3 * n + 2n * n) + -6 = 2n2 + -5(n + 6)
(3n + 2n2) + -6 = 2n2 + -5(n + 6)

Reorder the terms:
-6 + 3n + 2n2 = 2n2 + -5(n + 6)

Reorder the terms:
-6 + 3n + 2n2 = 2n2 + -5(6 + n)
-6 + 3n + 2n2 = 2n2 + (6 * -5 + n * -5)
-6 + 3n + 2n2 = 2n2 + (-30 + -5n)

Reorder the terms:
-6 + 3n + 2n2 = -30 + -5n + 2n2

Add '-2n2' to each side of the equation.
-6 + 3n + 2n2 + -2n2 = -30 + -5n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-6 + 3n + 0 = -30 + -5n + 2n2 + -2n2
-6 + 3n = -30 + -5n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-6 + 3n = -30 + -5n + 0
-6 + 3n = -30 + -5n

Solving
-6 + 3n = -30 + -5n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '5n' to each side of the equation.
-6 + 3n + 5n = -30 + -5n + 5n

Combine like terms: 3n + 5n = 8n
-6 + 8n = -30 + -5n + 5n

Combine like terms: -5n + 5n = 0
-6 + 8n = -30 + 0
-6 + 8n = -30

Add '6' to each side of the equation.
-6 + 6 + 8n = -30 + 6

Combine like terms: -6 + 6 = 0
0 + 8n = -30 + 6
8n = -30 + 6

Combine like terms: -30 + 6 = -24
8n = -24

Divide each side by '8'.
n = -3

Simplifying
n = -3

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