(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.
(-7 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-7, 6}