(2a+3)(a-4)=

Solution for (2a+3)(a-4)= equation:

Simplifying
(2a + 3)(a + -4) = 0

Reorder the terms:
(3 + 2a)(a + -4) = 0

Reorder the terms:
(3 + 2a)(-4 + a) = 0

Multiply (3 + 2a) * (-4 + a)
(3(-4 + a) + 2a * (-4 + a)) = 0
((-4 * 3 + a * 3) + 2a * (-4 + a)) = 0
((-12 + 3a) + 2a * (-4 + a)) = 0
(-12 + 3a + (-4 * 2a + a * 2a)) = 0
(-12 + 3a + (-8a + 2a2)) = 0

Combine like terms: 3a + -8a = -5a
(-12 + -5a + 2a2) = 0

Solving
-12 + -5a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -2a)(4 + -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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-1.5, 4}