(3z+1)2=(2z-3)2+(12)2

Solution for (3z+1)2=(2z-3)2+(12)2 equation:

Simplifying
(3z + 1) * 2 = (2z + -3) * 2 + (12) * 2

Reorder the terms:
(1 + 3z) * 2 = (2z + -3) * 2 + (12) * 2

Reorder the terms for easier multiplication:
2(1 + 3z) = (2z + -3) * 2 + (12) * 2
(1 * 2 + 3z * 2) = (2z + -3) * 2 + (12) * 2
(2 + 6z) = (2z + -3) * 2 + (12) * 2

Reorder the terms:
2 + 6z = (-3 + 2z) * 2 + (12) * 2

Reorder the terms for easier multiplication:
2 + 6z = 2(-3 + 2z) + (12) * 2
2 + 6z = (-3 * 2 + 2z * 2) + (12) * 2
2 + 6z = (-6 + 4z) + (12) * 2

Multiply 12 * 2
2 + 6z = -6 + 4z + 24

Reorder the terms:
2 + 6z = -6 + 24 + 4z

Combine like terms: -6 + 24 = 18
2 + 6z = 18 + 4z

Solving
2 + 6z = 18 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
2 + 6z + -4z = 18 + 4z + -4z

Combine like terms: 6z + -4z = 2z
2 + 2z = 18 + 4z + -4z

Combine like terms: 4z + -4z = 0
2 + 2z = 18 + 0
2 + 2z = 18

Add '-2' to each side of the equation.
2 + -2 + 2z = 18 + -2

Combine like terms: 2 + -2 = 0
0 + 2z = 18 + -2
2z = 18 + -2

Combine like terms: 18 + -2 = 16
2z = 16

Divide each side by '2'.
z = 8

Simplifying
z = 8