(x-1)(x+2)=4

Solution for (x-1)(x+2)=4 equation:

Simplifying
(x + -1)(x + 2) = 4

Reorder the terms:
(-1 + x)(x + 2) = 4

Reorder the terms:
(-1 + x)(2 + x) = 4

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

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) = 4

Solving
-2 + 1x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
-2 + -4 + 1x + x2 = 4 + -4

Combine like terms: -2 + -4 = -6
-6 + 1x + x2 = 4 + -4

Combine like terms: 4 + -4 = 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}