(x+1)(4-x)=0

Solution for (x+1)(4-x)=0 equation:

Simplifying
(x + 1)(4 + -1x) = 0

Reorder the terms:
(1 + x)(4 + -1x) = 0

Multiply (1 + x) * (4 + -1x)
(1(4 + -1x) + x(4 + -1x)) = 0
((4 * 1 + -1x * 1) + x(4 + -1x)) = 0
((4 + -1x) + x(4 + -1x)) = 0
(4 + -1x + (4 * x + -1x * x)) = 0
(4 + -1x + (4x + -1x2)) = 0

Combine like terms: -1x + 4x = 3x
(4 + 3x + -1x2) = 0

Solving
4 + 3x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(1 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {4, -1}