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

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

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

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

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

Multiply (-3 + 4a) * (2 + a)
(-3(2 + a) + 4a * (2 + a)) = 0
((2 * -3 + a * -3) + 4a * (2 + a)) = 0
((-6 + -3a) + 4a * (2 + a)) = 0
(-6 + -3a + (2 * 4a + a * 4a)) = 0
(-6 + -3a + (8a + 4a2)) = 0

Combine like terms: -3a + 8a = 5a
(-6 + 5a + 4a2) = 0

Solving
-6 + 5a + 4a2 = 0

Solving for variable 'a'.

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

Simplifying
3 + -4a = 0

Solving
3 + -4a = 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 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Solution
a = {-2, 0.75}