(a-3)(a-3)=16

Solution for (a-3)(a-3)=16 equation:

Simplifying
(a + -3)(a + -3) = 16

Reorder the terms:
(-3 + a)(a + -3) = 16

Reorder the terms:
(-3 + a)(-3 + a) = 16

Multiply (-3 + a) * (-3 + a)
(-3(-3 + a) + a(-3 + a)) = 16
((-3 * -3 + a * -3) + a(-3 + a)) = 16
((9 + -3a) + a(-3 + a)) = 16
(9 + -3a + (-3 * a + a * a)) = 16
(9 + -3a + (-3a + a2)) = 16

Combine like terms: -3a + -3a = -6a
(9 + -6a + a2) = 16

Solving
9 + -6a + a2 = 16

Solving for variable 'a'.

Reorder the terms:
9 + -16 + -6a + a2 = 16 + -16

Combine like terms: 9 + -16 = -7
-7 + -6a + a2 = 16 + -16

Combine like terms: 16 + -16 = 0
-7 + -6a + a2 = 0

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1a = 0 + 1

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

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

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

Simplifying
a = -1
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 = {-1, 7}