x(x-2)+((x+1)(x+2))=80

Solution for x(x-2)+((x+1)(x+2))=80 equation:

Simplifying
x(x + -2) + ((x + 1)(x + 2)) = 80

Reorder the terms:
x(-2 + x) + ((x + 1)(x + 2)) = 80
(-2 * x + x * x) + ((x + 1)(x + 2)) = 80
(-2x + x2) + ((x + 1)(x + 2)) = 80

Reorder the terms:
-2x + x2 + ((1 + x)(x + 2)) = 80

Reorder the terms:
-2x + x2 + ((1 + x)(2 + x)) = 80

Multiply (1 + x) * (2 + x)
-2x + x2 + ((1(2 + x) + x(2 + x))) = 80
-2x + x2 + (((2 * 1 + x * 1) + x(2 + x))) = 80
-2x + x2 + (((2 + 1x) + x(2 + x))) = 80
-2x + x2 + ((2 + 1x + (2 * x + x * x))) = 80
-2x + x2 + ((2 + 1x + (2x + x2))) = 80

Combine like terms: 1x + 2x = 3x
-2x + x2 + ((2 + 3x + x2)) = 80
-2x + x2 + (2 + 3x + x2) = 80

Remove parenthesis around (2 + 3x + x2)
-2x + x2 + 2 + 3x + x2 = 80

Reorder the terms:
2 + -2x + 3x + x2 + x2 = 80

Combine like terms: -2x + 3x = 1x
2 + 1x + x2 + x2 = 80

Combine like terms: x2 + x2 = 2x2
2 + 1x + 2x2 = 80

Solving
2 + 1x + 2x2 = 80

Solving for variable 'x'.

Reorder the terms:
2 + -80 + 1x + 2x2 = 80 + -80

Combine like terms: 2 + -80 = -78
-78 + 1x + 2x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-78 + 1x + 2x2 = 0

Factor a trinomial.
(-13 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5
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 = {-6.5, 6}