-5z(z+1)=-2z+10

Solution for -5z(z+1)=-2z+10 equation:

Simplifying
-5z(z + 1) = -2z + 10

Reorder the terms:
-5z(1 + z) = -2z + 10
(1 * -5z + z * -5z) = -2z + 10
(-5z + -5z2) = -2z + 10

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

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

Solving for variable 'z'.

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

Combine like terms: -5z + 2z = -3z
-10 + -3z + -5z2 = 10 + -2z + -10 + 2z

Reorder the terms:
-10 + -3z + -5z2 = 10 + -10 + -2z + 2z

Combine like terms: 10 + -10 = 0
-10 + -3z + -5z2 = 0 + -2z + 2z
-10 + -3z + -5z2 = -2z + 2z

Combine like terms: -2z + 2z = 0
-10 + -3z + -5z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 3z + 5z2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(10 + 3z + 5z2)' equal to zero and attempt to solve:

Simplifying
10 + 3z + 5z2 = 0

Solving
10 + 3z + 5z2 = 0

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

Divide each side by '5'.
2 + 0.6z + z2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.6z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 0.6z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.6z + z2 = 0 + -2
0.6z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.6z + z2 = -2

The z term is 0.6z.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6z + 0.09 + z2 = -2 + 0.09

Reorder the terms:
0.09 + 0.6z + z2 = -2 + 0.09

Combine like terms: -2 + 0.09 = -1.91
0.09 + 0.6z + z2 = -1.91

Factor a perfect square on the left side:
(z + 0.3)(z + 0.3) = -1.91

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.