(2n+1)(n-2)-(n+4)(n-3)=0

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Solution for (2n+1)(n-2)-(n+4)(n-3)=0 equation: 


Simplifying
(2n + 1)(n + -2) + -1(n + 4)(n + -3) = 0

Reorder the terms:
(1 + 2n)(n + -2) + -1(n + 4)(n + -3) = 0

Reorder the terms:
(1 + 2n)(-2 + n) + -1(n + 4)(n + -3) = 0

Multiply (1 + 2n) * (-2 + n)
(1(-2 + n) + 2n * (-2 + n)) + -1(n + 4)(n + -3) = 0
((-2 * 1 + n * 1) + 2n * (-2 + n)) + -1(n + 4)(n + -3) = 0
((-2 + 1n) + 2n * (-2 + n)) + -1(n + 4)(n + -3) = 0
(-2 + 1n + (-2 * 2n + n * 2n)) + -1(n + 4)(n + -3) = 0
(-2 + 1n + (-4n + 2n2)) + -1(n + 4)(n + -3) = 0

Combine like terms: 1n + -4n = -3n
(-2 + -3n + 2n2) + -1(n + 4)(n + -3) = 0

Reorder the terms:
-2 + -3n + 2n2 + -1(4 + n)(n + -3) = 0

Reorder the terms:
-2 + -3n + 2n2 + -1(4 + n)(-3 + n) = 0

Multiply (4 + n) * (-3 + n)
-2 + -3n + 2n2 + -1(4(-3 + n) + n(-3 + n)) = 0
-2 + -3n + 2n2 + -1((-3 * 4 + n * 4) + n(-3 + n)) = 0
-2 + -3n + 2n2 + -1((-12 + 4n) + n(-3 + n)) = 0
-2 + -3n + 2n2 + -1(-12 + 4n + (-3 * n + n * n)) = 0
-2 + -3n + 2n2 + -1(-12 + 4n + (-3n + n2)) = 0

Combine like terms: 4n + -3n = 1n
-2 + -3n + 2n2 + -1(-12 + 1n + n2) = 0
-2 + -3n + 2n2 + (-12 * -1 + 1n * -1 + n2 * -1) = 0
-2 + -3n + 2n2 + (12 + -1n + -1n2) = 0

Reorder the terms:
-2 + 12 + -3n + -1n + 2n2 + -1n2 = 0

Combine like terms: -2 + 12 = 10
10 + -3n + -1n + 2n2 + -1n2 = 0

Combine like terms: -3n + -1n = -4n
10 + -4n + 2n2 + -1n2 = 0

Combine like terms: 2n2 + -1n2 = 1n2
10 + -4n + 1n2 = 0

Solving
10 + -4n + 1n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -4n + -10 + n2 = 0 + -10

Reorder the terms:
10 + -10 + -4n + n2 = 0 + -10

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

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

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = -10 + 4

Reorder the terms:
4 + -4n + n2 = -10 + 4

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

Factor a perfect square on the left side:
(n + -2)(n + -2) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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