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

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

Simplifying
0 = (a + 2)(2a + -3)

Reorder the terms:
0 = (2 + a)(2a + -3)

Reorder the terms:
0 = (2 + a)(-3 + 2a)

Multiply (2 + a) * (-3 + 2a)
0 = (2(-3 + 2a) + a(-3 + 2a))
0 = ((-3 * 2 + 2a * 2) + a(-3 + 2a))
0 = ((-6 + 4a) + a(-3 + 2a))
0 = (-6 + 4a + (-3 * a + 2a * a))
0 = (-6 + 4a + (-3a + 2a2))

Combine like terms: 4a + -3a = 1a
0 = (-6 + 1a + 2a2)

Solving
0 = -6 + 1a + 2a2

Solving for variable 'a'.

Combine like terms: 0 + 6 = 6
6 + -1a + -2a2 = -6 + 1a + 2a2 + 6 + -1a + -2a2

Reorder the terms:
6 + -1a + -2a2 = -6 + 6 + 1a + -1a + 2a2 + -2a2

Combine like terms: -6 + 6 = 0
6 + -1a + -2a2 = 0 + 1a + -1a + 2a2 + -2a2
6 + -1a + -2a2 = 1a + -1a + 2a2 + -2a2

Combine like terms: 1a + -1a = 0
6 + -1a + -2a2 = 0 + 2a2 + -2a2
6 + -1a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
6 + -1a + -2a2 = 0

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

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

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

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

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

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

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

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

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

Simplifying
a = -2
Solution
a = {1.5, -2}