z^2-3z+24=-12

Solution for z^2-3z+24=-12 equation:

Simplifying
z2 + -3z + 24 = -12

Reorder the terms:
24 + -3z + z2 = -12

Solving
24 + -3z + z2 = -12

Solving for variable 'z'.

Reorder the terms:
24 + 12 + -3z + z2 = -12 + 12

Combine like terms: 24 + 12 = 36
36 + -3z + z2 = -12 + 12

Combine like terms: -12 + 12 = 0
36 + -3z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -3z + -36 + z2 = 0 + -36

Reorder the terms:
36 + -36 + -3z + z2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -3z + z2 = 0 + -36
-3z + z2 = 0 + -36

Combine like terms: 0 + -36 = -36
-3z + z2 = -36

The z term is -3z.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3z + 2.25 + z2 = -36 + 2.25

Reorder the terms:
2.25 + -3z + z2 = -36 + 2.25

Combine like terms: -36 + 2.25 = -33.75
2.25 + -3z + z2 = -33.75

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = -33.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.