(x-2)(x+2)-3(x+5)+1=0

Solution for (x-2)(x+2)-3(x+5)+1=0 equation:

Simplifying
(x + -2)(x + 2) + -3(x + 5) + 1 = 0

Reorder the terms:
(-2 + x)(x + 2) + -3(x + 5) + 1 = 0

Reorder the terms:
(-2 + x)(2 + x) + -3(x + 5) + 1 = 0

Multiply (-2 + x) * (2 + x)
(-2(2 + x) + x(2 + x)) + -3(x + 5) + 1 = 0
((2 * -2 + x * -2) + x(2 + x)) + -3(x + 5) + 1 = 0
((-4 + -2x) + x(2 + x)) + -3(x + 5) + 1 = 0
(-4 + -2x + (2 * x + x * x)) + -3(x + 5) + 1 = 0
(-4 + -2x + (2x + x2)) + -3(x + 5) + 1 = 0

Combine like terms: -2x + 2x = 0
(-4 + 0 + x2) + -3(x + 5) + 1 = 0
(-4 + x2) + -3(x + 5) + 1 = 0

Reorder the terms:
-4 + x2 + -3(5 + x) + 1 = 0
-4 + x2 + (5 * -3 + x * -3) + 1 = 0
-4 + x2 + (-15 + -3x) + 1 = 0

Reorder the terms:
-4 + -15 + 1 + -3x + x2 = 0

Combine like terms: -4 + -15 = -19
-19 + 1 + -3x + x2 = 0

Combine like terms: -19 + 1 = -18
-18 + -3x + x2 = 0

Solving
-18 + -3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3, 6}