5(a-4)3(a+1.5)=

Solution for 5(a-4)3(a+1.5)= equation:

Simplifying
5(a + -4) * 3(a + 1.5) = 0

Reorder the terms:
5(-4 + a) * 3(a + 1.5) = 0

Reorder the terms:
5(-4 + a) * 3(1.5 + a) = 0

Reorder the terms for easier multiplication:
5 * 3(-4 + a)(1.5 + a) = 0

Multiply 5 * 3
15(-4 + a)(1.5 + a) = 0

Multiply (-4 + a) * (1.5 + a)
15(-4(1.5 + a) + a(1.5 + a)) = 0
15((1.5 * -4 + a * -4) + a(1.5 + a)) = 0
15((-6 + -4a) + a(1.5 + a)) = 0
15(-6 + -4a + (1.5 * a + a * a)) = 0
15(-6 + -4a + (1.5a + a2)) = 0

Combine like terms: -4a + 1.5a = -2.5a
15(-6 + -2.5a + a2) = 0
(-6 * 15 + -2.5a * 15 + a2 * 15) = 0
(-90 + -37.5a + 15a2) = 0

Solving
-90 + -37.5a + 15a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
-6 + -2.5a + a2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2.5a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + -2.5a + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2.5a + a2 = 0 + 6
-2.5a + a2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2.5a + a2 = 6

The a term is -2.5a.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5a + 1.5625 + a2 = 6 + 1.5625

Reorder the terms:
1.5625 + -2.5a + a2 = 6 + 1.5625

Combine like terms: 6 + 1.5625 = 7.5625
1.5625 + -2.5a + a2 = 7.5625

Factor a perfect square on the left side:
(a + -1.25)(a + -1.25) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(a + -1.25) equal to 2.75 and -2.75.

Subproblem 1
a + -1.25 = 2.75

Simplifying
a + -1.25 = 2.75

Reorder the terms:
-1.25 + a = 2.75

Solving
-1.25 + a = 2.75

Solving for variable 'a'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + a = 2.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + a = 2.75 + 1.25
a = 2.75 + 1.25

Combine like terms: 2.75 + 1.25 = 4
a = 4

Simplifying
a = 4

Subproblem 2
a + -1.25 = -2.75

Simplifying
a + -1.25 = -2.75

Reorder the terms:
-1.25 + a = -2.75

Solving
-1.25 + a = -2.75

Solving for variable 'a'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + a = -2.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + a = -2.75 + 1.25
a = -2.75 + 1.25

Combine like terms: -2.75 + 1.25 = -1.5
a = -1.5

Simplifying
a = -1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4, -1.5}