Use the quadratic formula to solve. Express your answer in simplest form.6, z, squared, minus, 24, z, plus, 16, equals, minus, 3, z, squared6z 2 −24z+16=−3z 2

The given equation is 6z^2 - 24z + 16 = -3z^2.

First, we need to rearrange the equation to get all terms on one side. This gives us:

6z^2 + 3z^2 - 24z + 16 = 0

Simplify the equation:

9z^2 - 24z + 16 = 0

Now, we can use the quadratic formula to solve for z. The quadratic formula is:

z = [-b ± sqrt(b^2 - 4ac)] / 2a

In this equation, a = 9, b = -24, and c = 16.

Substitute these values into the quadratic formula:

z = [24 ± sqrt((-24)^2 - 4916)] / 2*9 z = [24 ± sqrt(576 - 576)] / 18 z = [24 ± sqrt(0)] / 18 z = [24 ± 0] / 18

So, the solutions are z = 24/18 = 4/3 and z = 0/18 = 0.

Therefore, the solutions to the equation 6z^2 - 24z + 16 = -3z^2 are z = 4/3 and z = 0.