16(2z^2+2z-1)=8

Solution for 16(2z^2+2z-1)=8 equation:

Simplifying
16(2z2 + 2z + -1) = 8

Reorder the terms:
16(-1 + 2z + 2z2) = 8
(-1 * 16 + 2z * 16 + 2z2 * 16) = 8
(-16 + 32z + 32z2) = 8

Solving
-16 + 32z + 32z2 = 8

Solving for variable 'z'.

Reorder the terms:
-16 + -8 + 32z + 32z2 = 8 + -8

Combine like terms: -16 + -8 = -24
-24 + 32z + 32z2 = 8 + -8

Combine like terms: 8 + -8 = 0
-24 + 32z + 32z2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-3 + 4z + 4z2) = 0

Factor a trinomial.
8((-3 + -2z)(1 + -2z)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-3 + -2z)' equal to zero and attempt to solve:

Simplifying
-3 + -2z = 0

Solving
-3 + -2z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2z = 0 + 3
-2z = 0 + 3

Combine like terms: 0 + 3 = 3
-2z = 3

Divide each side by '-2'.
z = -1.5

Simplifying
z = -1.5
Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-1.5, 0.5}