2a-3a+5=(a-1)(a+1)

Solution for 2a-3a+5=(a-1)(a+1) equation:

Simplifying
2a + -3a + 5 = (a + -1)(a + 1)

Reorder the terms:
5 + 2a + -3a = (a + -1)(a + 1)

Combine like terms: 2a + -3a = -1a
5 + -1a = (a + -1)(a + 1)

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

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

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

Combine like terms: -1a + 1a = 0
5 + -1a = (-1 + 0 + a2)
5 + -1a = (-1 + a2)

Solving
5 + -1a = -1 + a2

Solving for variable 'a'.

Reorder the terms:
5 + 1 + -1a + -1a2 = -1 + a2 + 1 + -1a2

Combine like terms: 5 + 1 = 6
6 + -1a + -1a2 = -1 + a2 + 1 + -1a2

Reorder the terms:
6 + -1a + -1a2 = -1 + 1 + a2 + -1a2

Combine like terms: -1 + 1 = 0
6 + -1a + -1a2 = 0 + a2 + -1a2
6 + -1a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
6 + -1a + -1a2 = 0

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

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

Divide each side by '-1'.
a = 2

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

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Solution
a = {2, -3}