0.4(2z+6)0.1=0.5(2z-3)

Solution for 0.4(2z+6)0.1=0.5(2z-3) equation:

Simplifying
0.4(2z + 6) * 0.1 = 0.5(2z + -3)

Reorder the terms:
0.4(6 + 2z) * 0.1 = 0.5(2z + -3)

Reorder the terms for easier multiplication:
0.4 * 0.1(6 + 2z) = 0.5(2z + -3)

Multiply 0.4 * 0.1
0.04(6 + 2z) = 0.5(2z + -3)
(6 * 0.04 + 2z * 0.04) = 0.5(2z + -3)
(0.24 + 0.08z) = 0.5(2z + -3)

Reorder the terms:
0.24 + 0.08z = 0.5(-3 + 2z)
0.24 + 0.08z = (-3 * 0.5 + 2z * 0.5)
0.24 + 0.08z = (-1.5 + 1z)

Solving
0.24 + 0.08z = -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.
0.24 + 0.08z + -1z = -1.5 + 1z + -1z

Combine like terms: 0.08z + -1z = -0.92z
0.24 + -0.92z = -1.5 + 1z + -1z

Combine like terms: 1z + -1z = 0
0.24 + -0.92z = -1.5 + 0
0.24 + -0.92z = -1.5

Add '-0.24' to each side of the equation.
0.24 + -0.24 + -0.92z = -1.5 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
0.00 + -0.92z = -1.5 + -0.24
-0.92z = -1.5 + -0.24

Combine like terms: -1.5 + -0.24 = -1.74
-0.92z = -1.74

Divide each side by '-0.92'.
z = 1.891304348

Simplifying
z = 1.891304348