6z 2 −24z+16=−3z 2

It seems like you want to solve the equation "6z^2 - 24z + 16 = -3z^2". Here are the steps:

Step 1: Combine like terms on both sides of the equation. This gives us "9z^2 - 24z + 16 = 0".

Step 2: Divide all terms by the coefficient of z^2, which is 9. This gives us "z^2 - (8/3)z + 16/9 = 0".

Step 3: Now, we can solve this quadratic equation using the quadratic formula, z = [-b ± sqrt(b^2 - 4ac)] / (2a). Here, a = 1, b = -8/3, and c = 16/9.

Step 4: Substitute a, b, and c into the quadratic formula. This gives us z = [(8/3) ± sqrt((8/3)^2 - 41(16/9))] / (2*1).

Step 5: Simplify the expression under the square root. This gives us z = [(8/3) ± sqrt((64/9) - (64/9))] / 2.

Step 6: Since the expression under the square root is zero, the two solutions are the same. So, z = (8/3) / 2 = 4/3.

So, the solution to the equation "6z^2 - 24z + 16 = -3z^2" is z = 4/3.