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

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

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

Reorder the terms:
5z + -3(5 + 4z) + 2(3 + -1z) = 2(z + -3) + -4(2 + -1z)
5z + (5 * -3 + 4z * -3) + 2(3 + -1z) = 2(z + -3) + -4(2 + -1z)
5z + (-15 + -12z) + 2(3 + -1z) = 2(z + -3) + -4(2 + -1z)
5z + -15 + -12z + (3 * 2 + -1z * 2) = 2(z + -3) + -4(2 + -1z)
5z + -15 + -12z + (6 + -2z) = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
-15 + 6 + 5z + -12z + -2z = 2(z + -3) + -4(2 + -1z)

Combine like terms: -15 + 6 = -9
-9 + 5z + -12z + -2z = 2(z + -3) + -4(2 + -1z)

Combine like terms: 5z + -12z = -7z
-9 + -7z + -2z = 2(z + -3) + -4(2 + -1z)

Combine like terms: -7z + -2z = -9z
-9 + -9z = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
-9 + -9z = 2(-3 + z) + -4(2 + -1z)
-9 + -9z = (-3 * 2 + z * 2) + -4(2 + -1z)
-9 + -9z = (-6 + 2z) + -4(2 + -1z)
-9 + -9z = -6 + 2z + (2 * -4 + -1z * -4)
-9 + -9z = -6 + 2z + (-8 + 4z)

Reorder the terms:
-9 + -9z = -6 + -8 + 2z + 4z

Combine like terms: -6 + -8 = -14
-9 + -9z = -14 + 2z + 4z

Combine like terms: 2z + 4z = 6z
-9 + -9z = -14 + 6z

Solving
-9 + -9z = -14 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
-9 + -9z + -6z = -14 + 6z + -6z

Combine like terms: -9z + -6z = -15z
-9 + -15z = -14 + 6z + -6z

Combine like terms: 6z + -6z = 0
-9 + -15z = -14 + 0
-9 + -15z = -14

Add '9' to each side of the equation.
-9 + 9 + -15z = -14 + 9

Combine like terms: -9 + 9 = 0
0 + -15z = -14 + 9
-15z = -14 + 9

Combine like terms: -14 + 9 = -5
-15z = -5

Divide each side by '-15'.
z = 0.3333333333

Simplifying
z = 0.3333333333