(7x-2)(3-x)=0

Solution for (7x-2)(3-x)=0 equation:

Simplifying
(7x + -2)(3 + -1x) = 0

Reorder the terms:
(-2 + 7x)(3 + -1x) = 0

Multiply (-2 + 7x) * (3 + -1x)
(-2(3 + -1x) + 7x * (3 + -1x)) = 0
((3 * -2 + -1x * -2) + 7x * (3 + -1x)) = 0
((-6 + 2x) + 7x * (3 + -1x)) = 0
(-6 + 2x + (3 * 7x + -1x * 7x)) = 0
(-6 + 2x + (21x + -7x2)) = 0

Combine like terms: 2x + 21x = 23x
(-6 + 23x + -7x2) = 0

Solving
-6 + 23x + -7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + x)(2 + -7x) = 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 '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {3, 0.2857142857}