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

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

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

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

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

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

Combine like terms: -7a + -3a = -10a
(21 + -10a + a2) = 0

Solving
21 + -10a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + -1a)(7 + -1a) = 0

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

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

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

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

Simplifying
a = 3
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 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 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {3, 7}