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

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

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

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

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

Multiply (4 + x) * (-1 + 4x)
(4(-1 + 4x) + x(-1 + 4x)) = 0
((-1 * 4 + 4x * 4) + x(-1 + 4x)) = 0
((-4 + 16x) + x(-1 + 4x)) = 0
(-4 + 16x + (-1 * x + 4x * x)) = 0
(-4 + 16x + (-1x + 4x2)) = 0

Combine like terms: 16x + -1x = 15x
(-4 + 15x + 4x2) = 0

Solving
-4 + 15x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x)(1 + -4x) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-4, 0.25}