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

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

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

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

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

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

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

Solving
-4 + -3x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 4}