(x-1)(2+x)=1120

Solution for (x-1)(2+x)=1120 equation:

Simplifying
(x + -1)(2 + x) = 1120

Reorder the terms:
(-1 + x)(2 + x) = 1120

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) = 1120
((2 * -1 + x * -1) + x(2 + x)) = 1120
((-2 + -1x) + x(2 + x)) = 1120
(-2 + -1x + (2 * x + x * x)) = 1120
(-2 + -1x + (2x + x2)) = 1120

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) = 1120

Solving
-2 + 1x + x2 = 1120

Solving for variable 'x'.

Reorder the terms:
-2 + -1120 + 1x + x2 = 1120 + -1120

Combine like terms: -2 + -1120 = -1122
-1122 + 1x + x2 = 1120 + -1120

Combine like terms: 1120 + -1120 = 0
-1122 + 1x + x2 = 0

Factor a trinomial.
(-34 + -1x)(33 + -1x) = 0

Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve:

Simplifying
-34 + -1x = 0

Solving
-34 + -1x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1x = 0 + 34
-1x = 0 + 34

Combine like terms: 0 + 34 = 34
-1x = 34

Divide each side by '-1'.
x = -34

Simplifying
x = -34
Subproblem 2
Set the factor '(33 + -1x)' equal to zero and attempt to solve:

Simplifying
33 + -1x = 0

Solving
33 + -1x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -1x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -1x = 0 + -33
-1x = 0 + -33

Combine like terms: 0 + -33 = -33
-1x = -33

Divide each side by '-1'.
x = 33

Simplifying
x = 33
Solution
x = {-34, 33}