10(-2z^2+4z+6)=0

Solution for 10(-2z^2+4z+6)=0 equation:

Simplifying
10(-2z2 + 4z + 6) = 0

Reorder the terms:
10(6 + 4z + -2z2) = 0
(6 * 10 + 4z * 10 + -2z2 * 10) = 0
(60 + 40z + -20z2) = 0

Solving
60 + 40z + -20z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '20'.
20(3 + 2z + -1z2) = 0

Factor a trinomial.
20((3 + -1z)(1 + z)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 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 + z = 0 + -1

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

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

Simplifying
z = -1
Solution
z = {3, -1}