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

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

Simplifying
(2a + 3)(a + -1) = 0

Reorder the terms:
(3 + 2a)(a + -1) = 0

Reorder the terms:
(3 + 2a)(-1 + a) = 0

Multiply (3 + 2a) * (-1 + a)
(3(-1 + a) + 2a * (-1 + a)) = 0
((-1 * 3 + a * 3) + 2a * (-1 + a)) = 0
((-3 + 3a) + 2a * (-1 + a)) = 0
(-3 + 3a + (-1 * 2a + a * 2a)) = 0
(-3 + 3a + (-2a + 2a2)) = 0

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

Solving
-3 + 1a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -2a)(1 + -1a) = 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 '(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
Solution
a = {-1.5, 1}