2(n+2)(2n-5)=3n+7

Solution for 2(n+2)(2n-5)=3n+7 equation:

Simplifying
2(n + 2)(2n + -5) = 3n + 7

Reorder the terms:
2(2 + n)(2n + -5) = 3n + 7

Reorder the terms:
2(2 + n)(-5 + 2n) = 3n + 7

Multiply (2 + n) * (-5 + 2n)
2(2(-5 + 2n) + n(-5 + 2n)) = 3n + 7
2((-5 * 2 + 2n * 2) + n(-5 + 2n)) = 3n + 7
2((-10 + 4n) + n(-5 + 2n)) = 3n + 7
2(-10 + 4n + (-5 * n + 2n * n)) = 3n + 7
2(-10 + 4n + (-5n + 2n2)) = 3n + 7

Combine like terms: 4n + -5n = -1n
2(-10 + -1n + 2n2) = 3n + 7
(-10 * 2 + -1n * 2 + 2n2 * 2) = 3n + 7
(-20 + -2n + 4n2) = 3n + 7

Reorder the terms:
-20 + -2n + 4n2 = 7 + 3n

Solving
-20 + -2n + 4n2 = 7 + 3n

Solving for variable 'n'.

Reorder the terms:
-20 + -7 + -2n + -3n + 4n2 = 7 + 3n + -7 + -3n

Combine like terms: -20 + -7 = -27
-27 + -2n + -3n + 4n2 = 7 + 3n + -7 + -3n

Combine like terms: -2n + -3n = -5n
-27 + -5n + 4n2 = 7 + 3n + -7 + -3n

Reorder the terms:
-27 + -5n + 4n2 = 7 + -7 + 3n + -3n

Combine like terms: 7 + -7 = 0
-27 + -5n + 4n2 = 0 + 3n + -3n
-27 + -5n + 4n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-27 + -5n + 4n2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-6.75 + -1.25n + n2 = 0

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + -1.25n + 6.75 + n2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + -1.25n + n2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + -1.25n + n2 = 0 + 6.75
-1.25n + n2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
-1.25n + n2 = 6.75

The n term is -1.25n.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25n + 0.390625 + n2 = 6.75 + 0.390625

Reorder the terms:
0.390625 + -1.25n + n2 = 6.75 + 0.390625

Combine like terms: 6.75 + 0.390625 = 7.140625
0.390625 + -1.25n + n2 = 7.140625

Factor a perfect square on the left side:
(n + -0.625)(n + -0.625) = 7.140625

Calculate the square root of the right side: 2.672194791

Break this problem into two subproblems by setting 
(n + -0.625) equal to 2.672194791 and -2.672194791.

Subproblem 1
n + -0.625 = 2.672194791

Simplifying
n + -0.625 = 2.672194791

Reorder the terms:
-0.625 + n = 2.672194791

Solving
-0.625 + n = 2.672194791

Solving for variable 'n'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + n = 2.672194791 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + n = 2.672194791 + 0.625
n = 2.672194791 + 0.625

Combine like terms: 2.672194791 + 0.625 = 3.297194791
n = 3.297194791

Simplifying
n = 3.297194791

Subproblem 2
n + -0.625 = -2.672194791

Simplifying
n + -0.625 = -2.672194791

Reorder the terms:
-0.625 + n = -2.672194791

Solving
-0.625 + n = -2.672194791

Solving for variable 'n'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + n = -2.672194791 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + n = -2.672194791 + 0.625
n = -2.672194791 + 0.625

Combine like terms: -2.672194791 + 0.625 = -2.047194791
n = -2.047194791

Simplifying
n = -2.047194791

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.297194791, -2.047194791}