3(2z-1)+4(z+3)=5(2z-1)+(3z-1)

Solution for 3(2z-1)+4(z+3)=5(2z-1)+(3z-1) equation:

Simplifying
3(2z + -1) + 4(z + 3) = 5(2z + -1) + (3z + -1)

Reorder the terms:
3(-1 + 2z) + 4(z + 3) = 5(2z + -1) + (3z + -1)
(-1 * 3 + 2z * 3) + 4(z + 3) = 5(2z + -1) + (3z + -1)
(-3 + 6z) + 4(z + 3) = 5(2z + -1) + (3z + -1)

Reorder the terms:
-3 + 6z + 4(3 + z) = 5(2z + -1) + (3z + -1)
-3 + 6z + (3 * 4 + z * 4) = 5(2z + -1) + (3z + -1)
-3 + 6z + (12 + 4z) = 5(2z + -1) + (3z + -1)

Reorder the terms:
-3 + 12 + 6z + 4z = 5(2z + -1) + (3z + -1)

Combine like terms: -3 + 12 = 9
9 + 6z + 4z = 5(2z + -1) + (3z + -1)

Combine like terms: 6z + 4z = 10z
9 + 10z = 5(2z + -1) + (3z + -1)

Reorder the terms:
9 + 10z = 5(-1 + 2z) + (3z + -1)
9 + 10z = (-1 * 5 + 2z * 5) + (3z + -1)
9 + 10z = (-5 + 10z) + (3z + -1)

Reorder the terms:
9 + 10z = -5 + 10z + (-1 + 3z)

Remove parenthesis around (-1 + 3z)
9 + 10z = -5 + 10z + -1 + 3z

Reorder the terms:
9 + 10z = -5 + -1 + 10z + 3z

Combine like terms: -5 + -1 = -6
9 + 10z = -6 + 10z + 3z

Combine like terms: 10z + 3z = 13z
9 + 10z = -6 + 13z

Solving
9 + 10z = -6 + 13z

Solving for variable 'z'.

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

Add '-13z' to each side of the equation.
9 + 10z + -13z = -6 + 13z + -13z

Combine like terms: 10z + -13z = -3z
9 + -3z = -6 + 13z + -13z

Combine like terms: 13z + -13z = 0
9 + -3z = -6 + 0
9 + -3z = -6

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

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

Combine like terms: -6 + -9 = -15
-3z = -15

Divide each side by '-3'.
z = 5

Simplifying
z = 5