2.5x(x+2)+4.5x=1.5(x-4)

Solution for 2.5x(x+2)+4.5x=1.5(x-4) equation:

Simplifying
2.5x(x + 2) + 4.5x = 1.5(x + -4)

Reorder the terms:
2.5x(2 + x) + 4.5x = 1.5(x + -4)
(2 * 2.5x + x * 2.5x) + 4.5x = 1.5(x + -4)
(5x + 2.5x2) + 4.5x = 1.5(x + -4)

Reorder the terms:
5x + 4.5x + 2.5x2 = 1.5(x + -4)

Combine like terms: 5x + 4.5x = 9.5x
9.5x + 2.5x2 = 1.5(x + -4)

Reorder the terms:
9.5x + 2.5x2 = 1.5(-4 + x)
9.5x + 2.5x2 = (-4 * 1.5 + x * 1.5)
9.5x + 2.5x2 = (-6 + 1.5x)

Solving
9.5x + 2.5x2 = -6 + 1.5x

Solving for variable 'x'.

Reorder the terms:
6 + 9.5x + -1.5x + 2.5x2 = -6 + 1.5x + 6 + -1.5x

Combine like terms: 9.5x + -1.5x = 8x
6 + 8x + 2.5x2 = -6 + 1.5x + 6 + -1.5x

Reorder the terms:
6 + 8x + 2.5x2 = -6 + 6 + 1.5x + -1.5x

Combine like terms: -6 + 6 = 0
6 + 8x + 2.5x2 = 0 + 1.5x + -1.5x
6 + 8x + 2.5x2 = 1.5x + -1.5x

Combine like terms: 1.5x + -1.5x = 0.0
6 + 8x + 2.5x2 = 0.0

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

Divide each side by '2.5'.
2.4 + 3.2x + x2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + 3.2x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + 3.2x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + 3.2x + x2 = 0 + -2.4
3.2x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
3.2x + x2 = -2.4

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = -2.4 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = -2.4 + 2.56

Combine like terms: -2.4 + 2.56 = 0.16
2.56 + 3.2x + x2 = 0.16

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(x + 1.6) equal to 0.4 and -0.4.

Subproblem 1
x + 1.6 = 0.4

Simplifying
x + 1.6 = 0.4

Reorder the terms:
1.6 + x = 0.4

Solving
1.6 + x = 0.4

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = 0.4 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = 0.4 + -1.6
x = 0.4 + -1.6

Combine like terms: 0.4 + -1.6 = -1.2
x = -1.2

Simplifying
x = -1.2

Subproblem 2
x + 1.6 = -0.4

Simplifying
x + 1.6 = -0.4

Reorder the terms:
1.6 + x = -0.4

Solving
1.6 + x = -0.4

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = -0.4 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = -0.4 + -1.6
x = -0.4 + -1.6

Combine like terms: -0.4 + -1.6 = -2
x = -2

Simplifying
x = -2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.2, -2}