(x-1)(x+2)=28

Solution for (x-1)(x+2)=28 equation:

Simplifying
(x + -1)(x + 2) = 28

Reorder the terms:
(-1 + x)(x + 2) = 28

Reorder the terms:
(-1 + x)(2 + x) = 28

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) = 28
((2 * -1 + x * -1) + x(2 + x)) = 28
((-2 + -1x) + x(2 + x)) = 28
(-2 + -1x + (2 * x + x * x)) = 28
(-2 + -1x + (2x + x2)) = 28

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) = 28

Solving
-2 + 1x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
-2 + -28 + 1x + x2 = 28 + -28

Combine like terms: -2 + -28 = -30
-30 + 1x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-30 + 1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}