(n+4)(n-3)=10

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Solution for (n+4)(n-3)=10 equation: 


Simplifying
(n + 4)(n + -3) = 10

Reorder the terms:
(4 + n)(n + -3) = 10

Reorder the terms:
(4 + n)(-3 + n) = 10

Multiply (4 + n) * (-3 + n)
(4(-3 + n) + n(-3 + n)) = 10
((-3 * 4 + n * 4) + n(-3 + n)) = 10
((-12 + 4n) + n(-3 + n)) = 10
(-12 + 4n + (-3 * n + n * n)) = 10
(-12 + 4n + (-3n + n2)) = 10

Combine like terms: 4n + -3n = 1n
(-12 + 1n + n2) = 10

Solving
-12 + 1n + n2 = 10

Solving for variable 'n'.

Reorder the terms:
-12 + -10 + 1n + n2 = 10 + -10

Combine like terms: -12 + -10 = -22
-22 + 1n + n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-22 + 1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 1n + 22 + n2 = 0 + 22

Reorder the terms:
-22 + 22 + 1n + n2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 1n + n2 = 0 + 22
1n + n2 = 0 + 22

Combine like terms: 0 + 22 = 22
1n + n2 = 22

The n term is 1n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
n + 0.25 + n2 = 22 + 0.25

Reorder the terms:
0.25 + n + n2 = 22 + 0.25

Combine like terms: 22 + 0.25 = 22.25
0.25 + n + n2 = 22.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(n + 0.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
n + 0.5 = 4.716990566

Simplifying
n + 0.5 = 4.716990566

Reorder the terms:
0.5 + n = 4.716990566

Solving
0.5 + n = 4.716990566

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 4.716990566 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 4.716990566 + -0.5
n = 4.716990566 + -0.5

Combine like terms: 4.716990566 + -0.5 = 4.216990566
n = 4.216990566

Simplifying
n = 4.216990566


Subproblem 2
n + 0.5 = -4.716990566

Simplifying
n + 0.5 = -4.716990566

Reorder the terms:
0.5 + n = -4.716990566

Solving
0.5 + n = -4.716990566

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -4.716990566 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -4.716990566 + -0.5
n = -4.716990566 + -0.5

Combine like terms: -4.716990566 + -0.5 = -5.216990566
n = -5.216990566

Simplifying
n = -5.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.216990566, -5.216990566}

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