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

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

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

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

Multiply (3 + a) * (4 + -3a)
(3(4 + -3a) + a(4 + -3a)) = 0
((4 * 3 + -3a * 3) + a(4 + -3a)) = 0
((12 + -9a) + a(4 + -3a)) = 0
(12 + -9a + (4 * a + -3a * a)) = 0
(12 + -9a + (4a + -3a2)) = 0

Combine like terms: -9a + 4a = -5a
(12 + -5a + -3a2) = 0

Solving
12 + -5a + -3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + -3a)(3 + a) = 0

Subproblem 1
Set the factor '(4 + -3a)' equal to zero and attempt to solve:

Simplifying
4 + -3a = 0

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

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

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

Divide each side by '-3'.
a = 1.333333333

Simplifying
a = 1.333333333
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 = {1.333333333, -3}