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

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

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

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

Remove parenthesis around (2 + x)
2 + x + x(x + -3) = 1

Reorder the terms:
2 + x + x(-3 + x) = 1
2 + x + (-3 * x + x * x) = 1
2 + x + (-3x + x2) = 1

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

Solving
2 + -2x + x2 = 1

Solving for variable 'x'.

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {1, 1}