5z-3(4z+5)+2(3z-7)=2(z-3)-4(2-z)

Solution for 5z-3(4z+5)+2(3z-7)=2(z-3)-4(2-z) equation:

Simplifying
5z + -3(4z + 5) + 2(3z + -7) = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
5z + -3(5 + 4z) + 2(3z + -7) = 2(z + -3) + -4(2 + -1z)
5z + (5 * -3 + 4z * -3) + 2(3z + -7) = 2(z + -3) + -4(2 + -1z)
5z + (-15 + -12z) + 2(3z + -7) = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
5z + -15 + -12z + 2(-7 + 3z) = 2(z + -3) + -4(2 + -1z)
5z + -15 + -12z + (-7 * 2 + 3z * 2) = 2(z + -3) + -4(2 + -1z)
5z + -15 + -12z + (-14 + 6z) = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
-15 + -14 + 5z + -12z + 6z = 2(z + -3) + -4(2 + -1z)

Combine like terms: -15 + -14 = -29
-29 + 5z + -12z + 6z = 2(z + -3) + -4(2 + -1z)

Combine like terms: 5z + -12z = -7z
-29 + -7z + 6z = 2(z + -3) + -4(2 + -1z)

Combine like terms: -7z + 6z = -1z
-29 + -1z = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
-29 + -1z = 2(-3 + z) + -4(2 + -1z)
-29 + -1z = (-3 * 2 + z * 2) + -4(2 + -1z)
-29 + -1z = (-6 + 2z) + -4(2 + -1z)
-29 + -1z = -6 + 2z + (2 * -4 + -1z * -4)
-29 + -1z = -6 + 2z + (-8 + 4z)

Reorder the terms:
-29 + -1z = -6 + -8 + 2z + 4z

Combine like terms: -6 + -8 = -14
-29 + -1z = -14 + 2z + 4z

Combine like terms: 2z + 4z = 6z
-29 + -1z = -14 + 6z

Solving
-29 + -1z = -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.
-29 + -1z + -6z = -14 + 6z + -6z

Combine like terms: -1z + -6z = -7z
-29 + -7z = -14 + 6z + -6z

Combine like terms: 6z + -6z = 0
-29 + -7z = -14 + 0
-29 + -7z = -14

Add '29' to each side of the equation.
-29 + 29 + -7z = -14 + 29

Combine like terms: -29 + 29 = 0
0 + -7z = -14 + 29
-7z = -14 + 29

Combine like terms: -14 + 29 = 15
-7z = 15

Divide each side by '-7'.
z = -2.142857143

Simplifying
z = -2.142857143