(3n+5)(n-2)-3n(n+1)=6

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Solution for (3n+5)(n-2)-3n(n+1)=6 equation:


Simplifying
(3n + 5)(n + -2) + -3n(n + 1) = 6

Reorder the terms:
(5 + 3n)(n + -2) + -3n(n + 1) = 6

Reorder the terms:
(5 + 3n)(-2 + n) + -3n(n + 1) = 6

Multiply (5 + 3n) * (-2 + n)
(5(-2 + n) + 3n * (-2 + n)) + -3n(n + 1) = 6
((-2 * 5 + n * 5) + 3n * (-2 + n)) + -3n(n + 1) = 6
((-10 + 5n) + 3n * (-2 + n)) + -3n(n + 1) = 6
(-10 + 5n + (-2 * 3n + n * 3n)) + -3n(n + 1) = 6
(-10 + 5n + (-6n + 3n2)) + -3n(n + 1) = 6

Combine like terms: 5n + -6n = -1n
(-10 + -1n + 3n2) + -3n(n + 1) = 6

Reorder the terms:
-10 + -1n + 3n2 + -3n(1 + n) = 6
-10 + -1n + 3n2 + (1 * -3n + n * -3n) = 6
-10 + -1n + 3n2 + (-3n + -3n2) = 6

Reorder the terms:
-10 + -1n + -3n + 3n2 + -3n2 = 6

Combine like terms: -1n + -3n = -4n
-10 + -4n + 3n2 + -3n2 = 6

Combine like terms: 3n2 + -3n2 = 0
-10 + -4n + 0 = 6
-10 + -4n = 6

Solving
-10 + -4n = 6

Solving for variable 'n'.

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

Add '10' to each side of the equation.
-10 + 10 + -4n = 6 + 10

Combine like terms: -10 + 10 = 0
0 + -4n = 6 + 10
-4n = 6 + 10

Combine like terms: 6 + 10 = 16
-4n = 16

Divide each side by '-4'.
n = -4

Simplifying
n = -4

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