(x-3)(x-3)=16

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

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

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

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

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = 16
((-3 * -3 + x * -3) + x(-3 + x)) = 16
((9 + -3x) + x(-3 + x)) = 16
(9 + -3x + (-3 * x + x * x)) = 16
(9 + -3x + (-3x + x2)) = 16

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) = 16

Solving
9 + -6x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
9 + -16 + -6x + x2 = 16 + -16

Combine like terms: 9 + -16 = -7
-7 + -6x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-7 + -6x + x2 = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

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

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

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

Simplifying
x = 7
Solution
x = {-1, 7}