(x-3)=(x-3)(x-5)

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Solution for (x-3)=(x-3)(x-5) equation:


Simplifying
(x + -3) = (x + -3)(x + -5)

Reorder the terms:
(-3 + x) = (x + -3)(x + -5)

Remove parenthesis around (-3 + x)
-3 + x = (x + -3)(x + -5)

Reorder the terms:
-3 + x = (-3 + x)(x + -5)

Reorder the terms:
-3 + x = (-3 + x)(-5 + x)

Multiply (-3 + x) * (-5 + x)
-3 + x = (-3(-5 + x) + x(-5 + x))
-3 + x = ((-5 * -3 + x * -3) + x(-5 + x))
-3 + x = ((15 + -3x) + x(-5 + x))
-3 + x = (15 + -3x + (-5 * x + x * x))
-3 + x = (15 + -3x + (-5x + x2))

Combine like terms: -3x + -5x = -8x
-3 + x = (15 + -8x + x2)

Solving
-3 + x = 15 + -8x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -15 + x + 8x + -1x2 = 15 + -8x + x2 + -15 + 8x + -1x2

Combine like terms: -3 + -15 = -18
-18 + x + 8x + -1x2 = 15 + -8x + x2 + -15 + 8x + -1x2

Combine like terms: x + 8x = 9x
-18 + 9x + -1x2 = 15 + -8x + x2 + -15 + 8x + -1x2

Reorder the terms:
-18 + 9x + -1x2 = 15 + -15 + -8x + 8x + x2 + -1x2

Combine like terms: 15 + -15 = 0
-18 + 9x + -1x2 = 0 + -8x + 8x + x2 + -1x2
-18 + 9x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-18 + 9x + -1x2 = 0 + x2 + -1x2
-18 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + 9x + -1x2 = 0

Factor a trinomial.
(-6 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6

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 = {6, 3}

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