0=(2a+1)(a-1)

Solution for 0=(2a+1)(a-1) equation:

Simplifying
0 = (2a + 1)(a + -1)

Reorder the terms:
0 = (1 + 2a)(a + -1)

Reorder the terms:
0 = (1 + 2a)(-1 + a)

Multiply (1 + 2a) * (-1 + a)
0 = (1(-1 + a) + 2a * (-1 + a))
0 = ((-1 * 1 + a * 1) + 2a * (-1 + a))
0 = ((-1 + 1a) + 2a * (-1 + a))
0 = (-1 + 1a + (-1 * 2a + a * 2a))
0 = (-1 + 1a + (-2a + 2a2))

Combine like terms: 1a + -2a = -1a
0 = (-1 + -1a + 2a2)

Solving
0 = -1 + -1a + 2a2

Solving for variable 'a'.

Combine like terms: 0 + 1 = 1
1 + a + -2a2 = -1 + -1a + 2a2 + 1 + a + -2a2

Reorder the terms:
1 + a + -2a2 = -1 + 1 + -1a + a + 2a2 + -2a2

Combine like terms: -1 + 1 = 0
1 + a + -2a2 = 0 + -1a + a + 2a2 + -2a2
1 + a + -2a2 = -1a + a + 2a2 + -2a2

Combine like terms: -1a + a = 0
1 + a + -2a2 = 0 + 2a2 + -2a2
1 + a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
1 + a + -2a2 = 0

Factor a trinomial.
(1 + -1a)(1 + 2a) = 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 '(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
Solution
a = {1, -0.5}