x(x+3)-(x-2)2=10

Solution for x(x+3)-(x-2)2=10 equation:

Simplifying
x(x + 3) + -1(x + -2) * 2 = 10

Reorder the terms:
x(3 + x) + -1(x + -2) * 2 = 10
(3 * x + x * x) + -1(x + -2) * 2 = 10
(3x + x2) + -1(x + -2) * 2 = 10

Reorder the terms:
3x + x2 + -1(-2 + x) * 2 = 10

Reorder the terms for easier multiplication:
3x + x2 + -1 * 2(-2 + x) = 10

Multiply -1 * 2
3x + x2 + -2(-2 + x) = 10
3x + x2 + (-2 * -2 + x * -2) = 10
3x + x2 + (4 + -2x) = 10

Reorder the terms:
4 + 3x + -2x + x2 = 10

Combine like terms: 3x + -2x = 1x
4 + 1x + x2 = 10

Solving
4 + 1x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
4 + -10 + 1x + x2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + 1x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + 1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}