(3A-4)(A-2)=1

Solution for (3A-4)(A-2)=1 equation:

Simplifying
(3A + -4)(A + -2) = 1

Reorder the terms:
(-4 + 3A)(A + -2) = 1

Reorder the terms:
(-4 + 3A)(-2 + A) = 1

Multiply (-4 + 3A) * (-2 + A)
(-4(-2 + A) + 3A * (-2 + A)) = 1
((-2 * -4 + A * -4) + 3A * (-2 + A)) = 1
((8 + -4A) + 3A * (-2 + A)) = 1
(8 + -4A + (-2 * 3A + A * 3A)) = 1
(8 + -4A + (-6A + 3A2)) = 1

Combine like terms: -4A + -6A = -10A
(8 + -10A + 3A2) = 1

Solving
8 + -10A + 3A2 = 1

Solving for variable 'A'.

Reorder the terms:
8 + -1 + -10A + 3A2 = 1 + -1

Combine like terms: 8 + -1 = 7
7 + -10A + 3A2 = 1 + -1

Combine like terms: 1 + -1 = 0
7 + -10A + 3A2 = 0

Factor a trinomial.
(1 + -1A)(7 + -3A) = 0

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

Simplifying
1 + -1A = 0

Solving
1 + -1A = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1A = 0 + -1
-1A = 0 + -1

Combine like terms: 0 + -1 = -1
-1A = -1

Divide each side by '-1'.
A = 1

Simplifying
A = 1
Subproblem 2
Set the factor '(7 + -3A)' equal to zero and attempt to solve:

Simplifying
7 + -3A = 0

Solving
7 + -3A = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3A = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3A = 0 + -7
-3A = 0 + -7

Combine like terms: 0 + -7 = -7
-3A = -7

Divide each side by '-3'.
A = 2.333333333

Simplifying
A = 2.333333333
Solution
A = {1, 2.333333333}