-4z(-5z-10)=4(-2z-9)

Solution for -4z(-5z-10)=4(-2z-9) equation:

Simplifying
-4z(-5z + -10) = 4(-2z + -9)

Reorder the terms:
-4z(-10 + -5z) = 4(-2z + -9)
(-10 * -4z + -5z * -4z) = 4(-2z + -9)
(40z + 20z2) = 4(-2z + -9)

Reorder the terms:
40z + 20z2 = 4(-9 + -2z)
40z + 20z2 = (-9 * 4 + -2z * 4)
40z + 20z2 = (-36 + -8z)

Solving
40z + 20z2 = -36 + -8z

Solving for variable 'z'.

Reorder the terms:
36 + 40z + 8z + 20z2 = -36 + -8z + 36 + 8z

Combine like terms: 40z + 8z = 48z
36 + 48z + 20z2 = -36 + -8z + 36 + 8z

Reorder the terms:
36 + 48z + 20z2 = -36 + 36 + -8z + 8z

Combine like terms: -36 + 36 = 0
36 + 48z + 20z2 = 0 + -8z + 8z
36 + 48z + 20z2 = -8z + 8z

Combine like terms: -8z + 8z = 0
36 + 48z + 20z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 12z + 5z2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(9 + 12z + 5z2)' equal to zero and attempt to solve:

Simplifying
9 + 12z + 5z2 = 0

Solving
9 + 12z + 5z2 = 0

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

Divide each side by '5'.
1.8 + 2.4z + z2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + 2.4z + -1.8 + z2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + 2.4z + z2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + 2.4z + z2 = 0 + -1.8
2.4z + z2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
2.4z + z2 = -1.8

The z term is 2.4z.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4z + 1.44 + z2 = -1.8 + 1.44

Reorder the terms:
1.44 + 2.4z + z2 = -1.8 + 1.44

Combine like terms: -1.8 + 1.44 = -0.36
1.44 + 2.4z + z2 = -0.36

Factor a perfect square on the left side:
(z + 1.2)(z + 1.2) = -0.36

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.