10+5z(z-2)=-2z+2

Solution for 10+5z(z-2)=-2z+2 equation:

Simplifying
10 + 5z(z + -2) = -2z + 2

Reorder the terms:
10 + 5z(-2 + z) = -2z + 2
10 + (-2 * 5z + z * 5z) = -2z + 2
10 + (-10z + 5z2) = -2z + 2

Reorder the terms:
10 + -10z + 5z2 = 2 + -2z

Solving
10 + -10z + 5z2 = 2 + -2z

Solving for variable 'z'.

Reorder the terms:
10 + -2 + -10z + 2z + 5z2 = 2 + -2z + -2 + 2z

Combine like terms: 10 + -2 = 8
8 + -10z + 2z + 5z2 = 2 + -2z + -2 + 2z

Combine like terms: -10z + 2z = -8z
8 + -8z + 5z2 = 2 + -2z + -2 + 2z

Reorder the terms:
8 + -8z + 5z2 = 2 + -2 + -2z + 2z

Combine like terms: 2 + -2 = 0
8 + -8z + 5z2 = 0 + -2z + 2z
8 + -8z + 5z2 = -2z + 2z

Combine like terms: -2z + 2z = 0
8 + -8z + 5z2 = 0

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

Divide each side by '5'.
1.6 + -1.6z + z2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -1.6z + -1.6 + z2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -1.6z + z2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -1.6z + z2 = 0 + -1.6
-1.6z + z2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-1.6z + z2 = -1.6

The z term is -1.6z.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6z + 0.64 + z2 = -1.6 + 0.64

Reorder the terms:
0.64 + -1.6z + z2 = -1.6 + 0.64

Combine like terms: -1.6 + 0.64 = -0.96
0.64 + -1.6z + z2 = -0.96

Factor a perfect square on the left side:
(z + -0.8)(z + -0.8) = -0.96

Can't calculate square root of the right side.

The solution to this equation could not be determined.