(4x-1)(3x+6)=0

Solution for (4x-1)(3x+6)=0 equation:

Simplifying
(4x + -1)(3x + 6) = 0

Reorder the terms:
(-1 + 4x)(3x + 6) = 0

Reorder the terms:
(-1 + 4x)(6 + 3x) = 0

Multiply (-1 + 4x) * (6 + 3x)
(-1(6 + 3x) + 4x * (6 + 3x)) = 0
((6 * -1 + 3x * -1) + 4x * (6 + 3x)) = 0
((-6 + -3x) + 4x * (6 + 3x)) = 0
(-6 + -3x + (6 * 4x + 3x * 4x)) = 0
(-6 + -3x + (24x + 12x2)) = 0

Combine like terms: -3x + 24x = 21x
(-6 + 21x + 12x2) = 0

Solving
-6 + 21x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 7x + 4x2) = 0

Factor a trinomial.
3((-2 + -1x)(1 + -4x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 0.25}