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

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

Simplifying
(z + -2)(z + 3) = z2 + 6

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

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

Multiply (-2 + z) * (3 + z)
(-2(3 + z) + z(3 + z)) = z2 + 6
((3 * -2 + z * -2) + z(3 + z)) = z2 + 6
((-6 + -2z) + z(3 + z)) = z2 + 6
(-6 + -2z + (3 * z + z * z)) = z2 + 6
(-6 + -2z + (3z + z2)) = z2 + 6

Combine like terms: -2z + 3z = 1z
(-6 + 1z + z2) = z2 + 6

Reorder the terms:
-6 + 1z + z2 = 6 + z2

Add '-1z2' to each side of the equation.
-6 + 1z + z2 + -1z2 = 6 + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-6 + 1z + 0 = 6 + z2 + -1z2
-6 + 1z = 6 + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-6 + 1z = 6 + 0
-6 + 1z = 6

Solving
-6 + 1z = 6

Solving for variable 'z'.

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

Add '6' to each side of the equation.
-6 + 6 + 1z = 6 + 6

Combine like terms: -6 + 6 = 0
0 + 1z = 6 + 6
1z = 6 + 6

Combine like terms: 6 + 6 = 12
1z = 12

Divide each side by '1'.
z = 12

Simplifying
z = 12