3a(4a+3)x(2a-6)=

Solution for 3a(4a+3)x(2a-6)= equation:

Simplifying
3a(4a + 3) * x(2a + -6) = 0

Reorder the terms:
3a(3 + 4a) * x(2a + -6) = 0

Reorder the terms:
3a(3 + 4a) * x(-6 + 2a) = 0

Reorder the terms for easier multiplication:
3a * x(3 + 4a)(-6 + 2a) = 0

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

Multiply (3 + 4a) * (-6 + 2a)
3ax(3(-6 + 2a) + 4a * (-6 + 2a)) = 0
3ax((-6 * 3 + 2a * 3) + 4a * (-6 + 2a)) = 0
3ax((-18 + 6a) + 4a * (-6 + 2a)) = 0
3ax(-18 + 6a + (-6 * 4a + 2a * 4a)) = 0
3ax(-18 + 6a + (-24a + 8a2)) = 0

Combine like terms: 6a + -24a = -18a
3ax(-18 + -18a + 8a2) = 0
(-18 * 3ax + -18a * 3ax + 8a2 * 3ax) = 0
(-54ax + -54a2x + 24a3x) = 0

Solving
-54ax + -54a2x + 24a3x = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6ax'.
6ax(-9 + -9a + 4a2) = 0

Factor a trinomial.
6ax((-3 + -4a)(3 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'ax' equal to zero and attempt to solve:

Simplifying
ax = 0

Solving
ax = 0

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

Simplifying
ax = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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
Subproblem 3
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.75, 3}