(3a-7)(3-a)=0

Solution for (3a-7)(3-a)=0 equation:

Simplifying
(3a + -7)(3 + -1a) = 0

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

Multiply (-7 + 3a) * (3 + -1a)
(-7(3 + -1a) + 3a * (3 + -1a)) = 0
((3 * -7 + -1a * -7) + 3a * (3 + -1a)) = 0
((-21 + 7a) + 3a * (3 + -1a)) = 0
(-21 + 7a + (3 * 3a + -1a * 3a)) = 0
(-21 + 7a + (9a + -3a2)) = 0

Combine like terms: 7a + 9a = 16a
(-21 + 16a + -3a2) = 0

Solving
-21 + 16a + -3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + a)(7 + -3a) = 0

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

Simplifying
-3 + a = 0

Solving
-3 + a = 0

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

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

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

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

Simplifying
a = 3
Subproblem 2
Set the factor '(7 + -3a)' equal to zero and attempt to solve:

Simplifying
7 + -3a = 0

Solving
7 + -3a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a = 0 + -7
-3a = 0 + -7

Combine like terms: 0 + -7 = -7
-3a = -7

Divide each side by '-3'.
a = 2.333333333

Simplifying
a = 2.333333333
Solution
a = {3, 2.333333333}