(x-1)(3x-5)=1

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Solution for (x-1)(3x-5)=1 equation: 


Simplifying
(x + -1)(3x + -5) = 1

Reorder the terms:
(-1 + x)(3x + -5) = 1

Reorder the terms:
(-1 + x)(-5 + 3x) = 1

Multiply (-1 + x) * (-5 + 3x)
(-1(-5 + 3x) + x(-5 + 3x)) = 1
((-5 * -1 + 3x * -1) + x(-5 + 3x)) = 1
((5 + -3x) + x(-5 + 3x)) = 1
(5 + -3x + (-5 * x + 3x * x)) = 1
(5 + -3x + (-5x + 3x2)) = 1

Combine like terms: -3x + -5x = -8x
(5 + -8x + 3x2) = 1

Solving
5 + -8x + 3x2 = 1

Solving for variable 'x'.

Reorder the terms:
5 + -1 + -8x + 3x2 = 1 + -1

Combine like terms: 5 + -1 = 4
4 + -8x + 3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
4 + -8x + 3x2 = 0

Factor a trinomial.
(2 + -3x)(2 + -1x) = 0


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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
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
Solution
x = {0.6666666667, 2}

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