(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.
(-3 + -1x)(4 + -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 '(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
Solution
x = {-3, 4}