10z^2+3z-3=0

Solution for 10z^2+3z-3=0 equation:

Simplifying
10z2 + 3z + -3 = 0

Reorder the terms:
-3 + 3z + 10z2 = 0

Solving
-3 + 3z + 10z2 = 0

Solving for variable 'z'.

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

Divide each side by '10'.
-0.3 + 0.3z + z2 = 0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 0.3z + 0.3 + z2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 0.3z + z2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 0.3z + z2 = 0 + 0.3
0.3z + z2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
0.3z + z2 = 0.3

The z term is 0.3z.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3z + 0.0225 + z2 = 0.3 + 0.0225

Reorder the terms:
0.0225 + 0.3z + z2 = 0.3 + 0.0225

Combine like terms: 0.3 + 0.0225 = 0.3225
0.0225 + 0.3z + z2 = 0.3225

Factor a perfect square on the left side:
(z + 0.15)(z + 0.15) = 0.3225

Calculate the square root of the right side: 0.567890835

Break this problem into two subproblems by setting 
(z + 0.15) equal to 0.567890835 and -0.567890835.

Subproblem 1
z + 0.15 = 0.567890835

Simplifying
z + 0.15 = 0.567890835

Reorder the terms:
0.15 + z = 0.567890835

Solving
0.15 + z = 0.567890835

Solving for variable 'z'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + z = 0.567890835 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + z = 0.567890835 + -0.15
z = 0.567890835 + -0.15

Combine like terms: 0.567890835 + -0.15 = 0.417890835
z = 0.417890835

Simplifying
z = 0.417890835

Subproblem 2
z + 0.15 = -0.567890835

Simplifying
z + 0.15 = -0.567890835

Reorder the terms:
0.15 + z = -0.567890835

Solving
0.15 + z = -0.567890835

Solving for variable 'z'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + z = -0.567890835 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + z = -0.567890835 + -0.15
z = -0.567890835 + -0.15

Combine like terms: -0.567890835 + -0.15 = -0.717890835
z = -0.717890835

Simplifying
z = -0.717890835

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.417890835, -0.717890835}