(4x-1)(x+6)=0

Solution for (4x-1)(x+6)=0 equation:

Simplifying
(4x + -1)(x + 6) = 0

Reorder the terms:
(-1 + 4x)(x + 6) = 0

Reorder the terms:
(-1 + 4x)(6 + x) = 0

Multiply (-1 + 4x) * (6 + x)
(-1(6 + x) + 4x * (6 + x)) = 0
((6 * -1 + x * -1) + 4x * (6 + x)) = 0
((-6 + -1x) + 4x * (6 + x)) = 0
(-6 + -1x + (6 * 4x + x * 4x)) = 0
(-6 + -1x + (24x + 4x2)) = 0

Combine like terms: -1x + 24x = 23x
(-6 + 23x + 4x2) = 0

Solving
-6 + 23x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(1 + -4x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 0.25}