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

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

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

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

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

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

Combine like terms: -2x + 1x = -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.
(-5 + -1x)(6 + -1x) = 0

Subproblem 1
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
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 = {-5, 6}