12z^2+24z-61=35

Solution for 12z^2+24z-61=35 equation:

Simplifying
12z2 + 24z + -61 = 35

Reorder the terms:
-61 + 24z + 12z2 = 35

Solving
-61 + 24z + 12z2 = 35

Solving for variable 'z'.

Reorder the terms:
-61 + -35 + 24z + 12z2 = 35 + -35

Combine like terms: -61 + -35 = -96
-96 + 24z + 12z2 = 35 + -35

Combine like terms: 35 + -35 = 0
-96 + 24z + 12z2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-8 + 2z + z2) = 0

Factor a trinomial.
12((-4 + -1z)(2 + -1z)) = 0

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

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
Subproblem 2
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
Solution
z = {-4, 2}