2z^2-10z=-12

Solution for 2z^2-10z=-12 equation:

Simplifying
2z2 + -10z = -12

Reorder the terms:
-10z + 2z2 = -12

Solving
-10z + 2z2 = -12

Solving for variable 'z'.

Reorder the terms:
12 + -10z + 2z2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -10z + 2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -5z + z2) = 0

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

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Subproblem 2
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
Solution
z = {2, 3}