.5(4z+7)+8.3=.7(4z-6)

Solution for .5(4z+7)+8.3=.7(4z-6) equation:

Simplifying
0.5(4z + 7) + 8.3 = 0.7(4z + -6)

Reorder the terms:
0.5(7 + 4z) + 8.3 = 0.7(4z + -6)
(7 * 0.5 + 4z * 0.5) + 8.3 = 0.7(4z + -6)
(3.5 + 2z) + 8.3 = 0.7(4z + -6)

Reorder the terms:
3.5 + 8.3 + 2z = 0.7(4z + -6)

Combine like terms: 3.5 + 8.3 = 11.8
11.8 + 2z = 0.7(4z + -6)

Reorder the terms:
11.8 + 2z = 0.7(-6 + 4z)
11.8 + 2z = (-6 * 0.7 + 4z * 0.7)
11.8 + 2z = (-4.2 + 2.8z)

Solving
11.8 + 2z = -4.2 + 2.8z

Solving for variable 'z'.

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

Add '-2.8z' to each side of the equation.
11.8 + 2z + -2.8z = -4.2 + 2.8z + -2.8z

Combine like terms: 2z + -2.8z = -0.8z
11.8 + -0.8z = -4.2 + 2.8z + -2.8z

Combine like terms: 2.8z + -2.8z = 0.0
11.8 + -0.8z = -4.2 + 0.0
11.8 + -0.8z = -4.2

Add '-11.8' to each side of the equation.
11.8 + -11.8 + -0.8z = -4.2 + -11.8

Combine like terms: 11.8 + -11.8 = 0.0
0.0 + -0.8z = -4.2 + -11.8
-0.8z = -4.2 + -11.8

Combine like terms: -4.2 + -11.8 = -16
-0.8z = -16

Divide each side by '-0.8'.
z = 20

Simplifying
z = 20