(x-2)*(2x-3)=1

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Solution for (x-2)*(2x-3)=1 equation:


Simplifying
(x + -2)(2x + -3) = 1

Reorder the terms:
(-2 + x)(2x + -3) = 1

Reorder the terms:
(-2 + x)(-3 + 2x) = 1

Multiply (-2 + x) * (-3 + 2x)
(-2(-3 + 2x) + x(-3 + 2x)) = 1
((-3 * -2 + 2x * -2) + x(-3 + 2x)) = 1
((6 + -4x) + x(-3 + 2x)) = 1
(6 + -4x + (-3 * x + 2x * x)) = 1
(6 + -4x + (-3x + 2x2)) = 1

Combine like terms: -4x + -3x = -7x
(6 + -7x + 2x2) = 1

Solving
6 + -7x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
6 + -1 + -7x + 2x2 = 1 + -1

Combine like terms: 6 + -1 = 5
5 + -7x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
5 + -7x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -2x) = 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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1, 2.5}

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