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

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


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

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

Reorder the terms:
6n + 2n2 + -5(3 + n) = (n + -3)(2n + 5)
6n + 2n2 + (3 * -5 + n * -5) = (n + -3)(2n + 5)
6n + 2n2 + (-15 + -5n) = (n + -3)(2n + 5)

Reorder the terms:
-15 + 6n + -5n + 2n2 = (n + -3)(2n + 5)

Combine like terms: 6n + -5n = 1n
-15 + 1n + 2n2 = (n + -3)(2n + 5)

Reorder the terms:
-15 + 1n + 2n2 = (-3 + n)(2n + 5)

Reorder the terms:
-15 + 1n + 2n2 = (-3 + n)(5 + 2n)

Multiply (-3 + n) * (5 + 2n)
-15 + 1n + 2n2 = (-3(5 + 2n) + n(5 + 2n))
-15 + 1n + 2n2 = ((5 * -3 + 2n * -3) + n(5 + 2n))
-15 + 1n + 2n2 = ((-15 + -6n) + n(5 + 2n))
-15 + 1n + 2n2 = (-15 + -6n + (5 * n + 2n * n))
-15 + 1n + 2n2 = (-15 + -6n + (5n + 2n2))

Combine like terms: -6n + 5n = -1n
-15 + 1n + 2n2 = (-15 + -1n + 2n2)

Add '15' to each side of the equation.
-15 + 1n + 15 + 2n2 = -15 + -1n + 15 + 2n2

Reorder the terms:
-15 + 15 + 1n + 2n2 = -15 + -1n + 15 + 2n2

Combine like terms: -15 + 15 = 0
0 + 1n + 2n2 = -15 + -1n + 15 + 2n2
1n + 2n2 = -15 + -1n + 15 + 2n2

Reorder the terms:
1n + 2n2 = -15 + 15 + -1n + 2n2

Combine like terms: -15 + 15 = 0
1n + 2n2 = 0 + -1n + 2n2
1n + 2n2 = -1n + 2n2

Add '-2n2' to each side of the equation.
1n + 2n2 + -2n2 = -1n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
1n + 0 = -1n + 2n2 + -2n2
1n = -1n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
1n = -1n + 0
1n = -1n

Solving
1n = -1n

Solving for variable 'n'.

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

Add 'n' to each side of the equation.
1n + n = -1n + n

Combine like terms: 1n + n = 2n
2n = -1n + n

Combine like terms: -1n + n = 0
2n = 0

Divide each side by '2'.
n = 0

Simplifying
n = 0

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