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

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

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

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

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

Combine like terms: 1x + 12x = 13x
(-3 + 13x + -4x2) = 0

Solving
-3 + 13x + -4x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
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 = {3, 0.25}