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

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

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

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

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

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

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

Solving
3 + -13x + 4x2 = 0

Solving for variable 'x'.

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

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.25, 3}