(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 = 11x
(3 + 11x + -4x2) = 0

Solving
3 + 11x + -4x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
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}