(6a^2+4.5a)(2a-6)=

Solution for (6a^2+4.5a)(2a-6)= equation:

Simplifying
(6a2 + 4.5a)(2a + -6) = 0

Reorder the terms:
(4.5a + 6a2)(2a + -6) = 0

Reorder the terms:
(4.5a + 6a2)(-6 + 2a) = 0

Multiply (4.5a + 6a2) * (-6 + 2a)
(4.5a * (-6 + 2a) + 6a2 * (-6 + 2a)) = 0
((-6 * 4.5a + 2a * 4.5a) + 6a2 * (-6 + 2a)) = 0
((-27a + 9a2) + 6a2 * (-6 + 2a)) = 0
(-27a + 9a2 + (-6 * 6a2 + 2a * 6a2)) = 0
(-27a + 9a2 + (-36a2 + 12a3)) = 0

Combine like terms: 9a2 + -36a2 = -27a2
(-27a + -27a2 + 12a3) = 0

Solving
-27a + -27a2 + 12a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-9 + -9a + 4a2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
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, -0.75, 3}