0.3z(z+5)=-2.3(z-1.5)

Solution for 0.3z(z+5)=-2.3(z-1.5) equation:

Simplifying
0.3z(z + 5) = -2.3(z + -1.5)

Reorder the terms:
0.3z(5 + z) = -2.3(z + -1.5)
(5 * 0.3z + z * 0.3z) = -2.3(z + -1.5)
(1.5z + 0.3z2) = -2.3(z + -1.5)

Reorder the terms:
1.5z + 0.3z2 = -2.3(-1.5 + z)
1.5z + 0.3z2 = (-1.5 * -2.3 + z * -2.3)
1.5z + 0.3z2 = (3.45 + -2.3z)

Solving
1.5z + 0.3z2 = 3.45 + -2.3z

Solving for variable 'z'.

Reorder the terms:
-3.45 + 1.5z + 2.3z + 0.3z2 = 3.45 + -2.3z + -3.45 + 2.3z

Combine like terms: 1.5z + 2.3z = 3.8z
-3.45 + 3.8z + 0.3z2 = 3.45 + -2.3z + -3.45 + 2.3z

Reorder the terms:
-3.45 + 3.8z + 0.3z2 = 3.45 + -3.45 + -2.3z + 2.3z

Combine like terms: 3.45 + -3.45 = 0.00
-3.45 + 3.8z + 0.3z2 = 0.00 + -2.3z + 2.3z
-3.45 + 3.8z + 0.3z2 = -2.3z + 2.3z

Combine like terms: -2.3z + 2.3z = 0.0
-3.45 + 3.8z + 0.3z2 = 0.0

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

Divide each side by '0.3'.
-11.5 + 12.66666667z + z2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + 12.66666667z + 11.5 + z2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + 12.66666667z + z2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + 12.66666667z + z2 = 0 + 11.5
12.66666667z + z2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
12.66666667z + z2 = 11.5

The z term is 12.66666667z.  Take half its coefficient (6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
12.66666667z + 40.11111113 + z2 = 11.5 + 40.11111113

Reorder the terms:
40.11111113 + 12.66666667z + z2 = 11.5 + 40.11111113

Combine like terms: 11.5 + 40.11111113 = 51.61111113
40.11111113 + 12.66666667z + z2 = 51.61111113

Factor a perfect square on the left side:
(z + 6.333333335)(z + 6.333333335) = 51.61111113

Calculate the square root of the right side: 7.184087355

Break this problem into two subproblems by setting 
(z + 6.333333335) equal to 7.184087355 and -7.184087355.

Subproblem 1
z + 6.333333335 = 7.184087355

Simplifying
z + 6.333333335 = 7.184087355

Reorder the terms:
6.333333335 + z = 7.184087355

Solving
6.333333335 + z = 7.184087355

Solving for variable 'z'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + z = 7.184087355 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + z = 7.184087355 + -6.333333335
z = 7.184087355 + -6.333333335

Combine like terms: 7.184087355 + -6.333333335 = 0.85075402
z = 0.85075402

Simplifying
z = 0.85075402

Subproblem 2
z + 6.333333335 = -7.184087355

Simplifying
z + 6.333333335 = -7.184087355

Reorder the terms:
6.333333335 + z = -7.184087355

Solving
6.333333335 + z = -7.184087355

Solving for variable 'z'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + z = -7.184087355 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + z = -7.184087355 + -6.333333335
z = -7.184087355 + -6.333333335

Combine like terms: -7.184087355 + -6.333333335 = -13.51742069
z = -13.51742069

Simplifying
z = -13.51742069

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.85075402, -13.51742069}