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

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

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

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

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

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

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

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

Solving
-3 + x = 9 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -9 + x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: -3 + -9 = -12
-12 + x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: x + 6x = 7x
-12 + 7x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Reorder the terms:
-12 + 7x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-12 + 7x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-12 + 7x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-12 + 7x + -1x2 = 0 + x2 + -1x2
-12 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 7x + -1x2 = 0

Factor a trinomial.
(-4 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Solution
x = {4, 3}