(1x-3)(x-3)=1

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Solution for (1x-3)(x-3)=1 equation:


Simplifying
(1x + -3)(x + -3) = 1

Reorder the terms:
(-3 + 1x)(x + -3) = 1

Reorder the terms:
(-3 + 1x)(-3 + x) = 1

Multiply (-3 + 1x) * (-3 + x)
(-3(-3 + x) + 1x * (-3 + x)) = 1
((-3 * -3 + x * -3) + 1x * (-3 + x)) = 1
((9 + -3x) + 1x * (-3 + x)) = 1
(9 + -3x + (-3 * 1x + x * 1x)) = 1
(9 + -3x + (-3x + 1x2)) = 1

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

Solving
9 + -6x + 1x2 = 1

Solving for variable 'x'.

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

Combine like terms: 9 + -1 = 8
8 + -6x + 1x2 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + -6x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {2, 4}

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