(x+1)(x-2)=40

Solution for (x+1)(x-2)=40 equation:

Simplifying
(x + 1)(x + -2) = 40

Reorder the terms:
(1 + x)(x + -2) = 40

Reorder the terms:
(1 + x)(-2 + x) = 40

Multiply (1 + x) * (-2 + x)
(1(-2 + x) + x(-2 + x)) = 40
((-2 * 1 + x * 1) + x(-2 + x)) = 40
((-2 + 1x) + x(-2 + x)) = 40
(-2 + 1x + (-2 * x + x * x)) = 40
(-2 + 1x + (-2x + x2)) = 40

Combine like terms: 1x + -2x = -1x
(-2 + -1x + x2) = 40

Solving
-2 + -1x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-2 + -40 + -1x + x2 = 40 + -40

Combine like terms: -2 + -40 = -42
-42 + -1x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-42 + -1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(7 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-6, 7}