(x-1)(x+2)=10

Solution for (x-1)(x+2)=10 equation:

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

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

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

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

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) = 10

Solving
-2 + 1x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-2 + -10 + 1x + x2 = 10 + -10

Combine like terms: -2 + -10 = -12
-12 + 1x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-12 + 1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
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
Solution
x = {-4, 3}