3z(z+2)=3z*3z+6z-3

Solution for 3z(z+2)=3z*3z+6z-3 equation:

Simplifying
3z(z + 2) = 3z * 3z + 6z + -3

Reorder the terms:
3z(2 + z) = 3z * 3z + 6z + -3
(2 * 3z + z * 3z) = 3z * 3z + 6z + -3
(6z + 3z2) = 3z * 3z + 6z + -3

Reorder the terms for easier multiplication:
6z + 3z2 = 3 * 3z * z + 6z + -3

Multiply 3 * 3
6z + 3z2 = 9z * z + 6z + -3

Multiply z * z
6z + 3z2 = 9z2 + 6z + -3

Reorder the terms:
6z + 3z2 = -3 + 6z + 9z2

Add '-6z' to each side of the equation.
6z + -6z + 3z2 = -3 + 6z + -6z + 9z2

Combine like terms: 6z + -6z = 0
0 + 3z2 = -3 + 6z + -6z + 9z2
3z2 = -3 + 6z + -6z + 9z2

Combine like terms: 6z + -6z = 0
3z2 = -3 + 0 + 9z2
3z2 = -3 + 9z2

Solving
3z2 = -3 + 9z2

Solving for variable 'z'.

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

Add '-9z2' to each side of the equation.
3z2 + -9z2 = -3 + 9z2 + -9z2

Combine like terms: 3z2 + -9z2 = -6z2
-6z2 = -3 + 9z2 + -9z2

Combine like terms: 9z2 + -9z2 = 0
-6z2 = -3 + 0
-6z2 = -3

Divide each side by '-6'.
z2 = 0.5

Simplifying
z2 = 0.5

Take the square root of each side:
z = {-0.707106781, 0.707106781}