(x+2)(x-2)-(x+1)2=-15

Solution for (x+2)(x-2)-(x+1)2=-15 equation:

Simplifying
(x + 2)(x + -2) + -1(x + 1) * 2 = -15

Reorder the terms:
(2 + x)(x + -2) + -1(x + 1) * 2 = -15

Reorder the terms:
(2 + x)(-2 + x) + -1(x + 1) * 2 = -15

Multiply (2 + x) * (-2 + x)
(2(-2 + x) + x(-2 + x)) + -1(x + 1) * 2 = -15
((-2 * 2 + x * 2) + x(-2 + x)) + -1(x + 1) * 2 = -15
((-4 + 2x) + x(-2 + x)) + -1(x + 1) * 2 = -15
(-4 + 2x + (-2 * x + x * x)) + -1(x + 1) * 2 = -15
(-4 + 2x + (-2x + x2)) + -1(x + 1) * 2 = -15

Combine like terms: 2x + -2x = 0
(-4 + 0 + x2) + -1(x + 1) * 2 = -15
(-4 + x2) + -1(x + 1) * 2 = -15

Reorder the terms:
-4 + x2 + -1(1 + x) * 2 = -15

Reorder the terms for easier multiplication:
-4 + x2 + -1 * 2(1 + x) = -15

Multiply -1 * 2
-4 + x2 + -2(1 + x) = -15
-4 + x2 + (1 * -2 + x * -2) = -15
-4 + x2 + (-2 + -2x) = -15

Reorder the terms:
-4 + -2 + -2x + x2 = -15

Combine like terms: -4 + -2 = -6
-6 + -2x + x2 = -15

Solving
-6 + -2x + x2 = -15

Solving for variable 'x'.

Reorder the terms:
-6 + 15 + -2x + x2 = -15 + 15

Combine like terms: -6 + 15 = 9
9 + -2x + x2 = -15 + 15

Combine like terms: -15 + 15 = 0
9 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -2x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -2x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x + x2 = 0 + -9
-2x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-2x + x2 = -9

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -9 + 1

Reorder the terms:
1 + -2x + x2 = -9 + 1

Combine like terms: -9 + 1 = -8
1 + -2x + x2 = -8

Factor a perfect square on the left side:
(x + -1)(x + -1) = -8

Can't calculate square root of the right side.

The solution to this equation could not be determined.