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

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

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

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

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

Combine like terms: 4x + 3x = 7x
(-12 + 7x + -1x2) = 0

Solving
-12 + 7x + -1x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
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 = {4, 3}