24z^2+42z-45=0

Solution for 24z^2+42z-45=0 equation:

Simplifying
24z2 + 42z + -45 = 0

Reorder the terms:
-45 + 42z + 24z2 = 0

Solving
-45 + 42z + 24z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 14z + 8z2) = 0

Factor a trinomial.
3((-5 + -2z)(3 + -4z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2z)' equal to zero and attempt to solve:

Simplifying
-5 + -2z = 0

Solving
-5 + -2z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2z = 0 + 5
-2z = 0 + 5

Combine like terms: 0 + 5 = 5
-2z = 5

Divide each side by '-2'.
z = -2.5

Simplifying
z = -2.5
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-2.5, 0.75}