0.4z(4z+7)+10.7=0.5(4z-5)

Solution for 0.4z(4z+7)+10.7=0.5(4z-5) equation:

Simplifying
0.4z(4z + 7) + 10.7 = 0.5(4z + -5)

Reorder the terms:
0.4z(7 + 4z) + 10.7 = 0.5(4z + -5)
(7 * 0.4z + 4z * 0.4z) + 10.7 = 0.5(4z + -5)
(2.8z + 1.6z2) + 10.7 = 0.5(4z + -5)

Reorder the terms:
10.7 + 2.8z + 1.6z2 = 0.5(4z + -5)

Reorder the terms:
10.7 + 2.8z + 1.6z2 = 0.5(-5 + 4z)
10.7 + 2.8z + 1.6z2 = (-5 * 0.5 + 4z * 0.5)
10.7 + 2.8z + 1.6z2 = (-2.5 + 2z)

Solving
10.7 + 2.8z + 1.6z2 = -2.5 + 2z

Solving for variable 'z'.

Reorder the terms:
10.7 + 2.5 + 2.8z + -2z + 1.6z2 = -2.5 + 2z + 2.5 + -2z

Combine like terms: 10.7 + 2.5 = 13.2
13.2 + 2.8z + -2z + 1.6z2 = -2.5 + 2z + 2.5 + -2z

Combine like terms: 2.8z + -2z = 0.8z
13.2 + 0.8z + 1.6z2 = -2.5 + 2z + 2.5 + -2z

Reorder the terms:
13.2 + 0.8z + 1.6z2 = -2.5 + 2.5 + 2z + -2z

Combine like terms: -2.5 + 2.5 = 0.0
13.2 + 0.8z + 1.6z2 = 0.0 + 2z + -2z
13.2 + 0.8z + 1.6z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
13.2 + 0.8z + 1.6z2 = 0

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

Divide each side by '1.6'.
8.25 + 0.5z + z2 = 0

Move the constant term to the right:

Add '-8.25' to each side of the equation.
8.25 + 0.5z + -8.25 + z2 = 0 + -8.25

Reorder the terms:
8.25 + -8.25 + 0.5z + z2 = 0 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + 0.5z + z2 = 0 + -8.25
0.5z + z2 = 0 + -8.25

Combine like terms: 0 + -8.25 = -8.25
0.5z + z2 = -8.25

The z term is 0.5z.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5z + 0.0625 + z2 = -8.25 + 0.0625

Reorder the terms:
0.0625 + 0.5z + z2 = -8.25 + 0.0625

Combine like terms: -8.25 + 0.0625 = -8.1875
0.0625 + 0.5z + z2 = -8.1875

Factor a perfect square on the left side:
(z + 0.25)(z + 0.25) = -8.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.