(x-1)(x+2)=54

Solution for (x-1)(x+2)=54 equation:

Simplifying
(x + -1)(x + 2) = 54

Reorder the terms:
(-1 + x)(x + 2) = 54

Reorder the terms:
(-1 + x)(2 + x) = 54

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) = 54
((2 * -1 + x * -1) + x(2 + x)) = 54
((-2 + -1x) + x(2 + x)) = 54
(-2 + -1x + (2 * x + x * x)) = 54
(-2 + -1x + (2x + x2)) = 54

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) = 54

Solving
-2 + 1x + x2 = 54

Solving for variable 'x'.

Reorder the terms:
-2 + -54 + 1x + x2 = 54 + -54

Combine like terms: -2 + -54 = -56
-56 + 1x + x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-56 + 1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
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
Solution
x = {-8, 7}