(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((-1 + -4x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-0.25, 2}