(x-1)(x+4)=104

Solution for (x-1)(x+4)=104 equation:

Simplifying
(x + -1)(x + 4) = 104

Reorder the terms:
(-1 + x)(x + 4) = 104

Reorder the terms:
(-1 + x)(4 + x) = 104

Multiply (-1 + x) * (4 + x)
(-1(4 + x) + x(4 + x)) = 104
((4 * -1 + x * -1) + x(4 + x)) = 104
((-4 + -1x) + x(4 + x)) = 104
(-4 + -1x + (4 * x + x * x)) = 104
(-4 + -1x + (4x + x2)) = 104

Combine like terms: -1x + 4x = 3x
(-4 + 3x + x2) = 104

Solving
-4 + 3x + x2 = 104

Solving for variable 'x'.

Reorder the terms:
-4 + -104 + 3x + x2 = 104 + -104

Combine like terms: -4 + -104 = -108
-108 + 3x + x2 = 104 + -104

Combine like terms: 104 + -104 = 0
-108 + 3x + x2 = 0

Factor a trinomial.
(-12 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-12, 9}