(2a-1)(a-2)=5

Solution for (2a-1)(a-2)=5 equation:

Simplifying
(2a + -1)(a + -2) = 5

Reorder the terms:
(-1 + 2a)(a + -2) = 5

Reorder the terms:
(-1 + 2a)(-2 + a) = 5

Multiply (-1 + 2a) * (-2 + a)
(-1(-2 + a) + 2a * (-2 + a)) = 5
((-2 * -1 + a * -1) + 2a * (-2 + a)) = 5
((2 + -1a) + 2a * (-2 + a)) = 5
(2 + -1a + (-2 * 2a + a * 2a)) = 5
(2 + -1a + (-4a + 2a2)) = 5

Combine like terms: -1a + -4a = -5a
(2 + -5a + 2a2) = 5

Solving
2 + -5a + 2a2 = 5

Solving for variable 'a'.

Reorder the terms:
2 + -5 + -5a + 2a2 = 5 + -5

Combine like terms: 2 + -5 = -3
-3 + -5a + 2a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-3 + -5a + 2a2 = 0

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.5, 3}