0.42(2z+6)+0.1=0.5(2z-3)

Solution for 0.42(2z+6)+0.1=0.5(2z-3) equation:

Simplifying
0.42(2z + 6) + 0.1 = 0.5(2z + -3)

Reorder the terms:
0.42(6 + 2z) + 0.1 = 0.5(2z + -3)
(6 * 0.42 + 2z * 0.42) + 0.1 = 0.5(2z + -3)
(2.52 + 0.84z) + 0.1 = 0.5(2z + -3)

Reorder the terms:
2.52 + 0.1 + 0.84z = 0.5(2z + -3)

Combine like terms: 2.52 + 0.1 = 2.62
2.62 + 0.84z = 0.5(2z + -3)

Reorder the terms:
2.62 + 0.84z = 0.5(-3 + 2z)
2.62 + 0.84z = (-3 * 0.5 + 2z * 0.5)
2.62 + 0.84z = (-1.5 + 1z)

Solving
2.62 + 0.84z = -1.5 + 1z

Solving for variable 'z'.

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

Add '-1z' to each side of the equation.
2.62 + 0.84z + -1z = -1.5 + 1z + -1z

Combine like terms: 0.84z + -1z = -0.16z
2.62 + -0.16z = -1.5 + 1z + -1z

Combine like terms: 1z + -1z = 0
2.62 + -0.16z = -1.5 + 0
2.62 + -0.16z = -1.5

Add '-2.62' to each side of the equation.
2.62 + -2.62 + -0.16z = -1.5 + -2.62

Combine like terms: 2.62 + -2.62 = 0.00
0.00 + -0.16z = -1.5 + -2.62
-0.16z = -1.5 + -2.62

Combine like terms: -1.5 + -2.62 = -4.12
-0.16z = -4.12

Divide each side by '-0.16'.
z = 25.75

Simplifying
z = 25.75