(a-3)(a-7)=

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

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

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

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

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

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