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

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

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

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

Combine like terms: 3 + -7 = -4
5z + -15 + -12z + 2(-4) = 2(z + -3) + -4(2 + -1z)

Multiply 2 * -4
5z + -15 + -12z + -8 = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
-15 + -8 + 5z + -12z = 2(z + -3) + -4(2 + -1z)

Combine like terms: -15 + -8 = -23
-23 + 5z + -12z = 2(z + -3) + -4(2 + -1z)

Combine like terms: 5z + -12z = -7z
-23 + -7z = 2(z + -3) + -4(2 + -1z)

Reorder the terms:
-23 + -7z = 2(-3 + z) + -4(2 + -1z)
-23 + -7z = (-3 * 2 + z * 2) + -4(2 + -1z)
-23 + -7z = (-6 + 2z) + -4(2 + -1z)
-23 + -7z = -6 + 2z + (2 * -4 + -1z * -4)
-23 + -7z = -6 + 2z + (-8 + 4z)

Reorder the terms:
-23 + -7z = -6 + -8 + 2z + 4z

Combine like terms: -6 + -8 = -14
-23 + -7z = -14 + 2z + 4z

Combine like terms: 2z + 4z = 6z
-23 + -7z = -14 + 6z

Solving
-23 + -7z = -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.
-23 + -7z + -6z = -14 + 6z + -6z

Combine like terms: -7z + -6z = -13z
-23 + -13z = -14 + 6z + -6z

Combine like terms: 6z + -6z = 0
-23 + -13z = -14 + 0
-23 + -13z = -14

Add '23' to each side of the equation.
-23 + 23 + -13z = -14 + 23

Combine like terms: -23 + 23 = 0
0 + -13z = -14 + 23
-13z = -14 + 23

Combine like terms: -14 + 23 = 9
-13z = 9

Divide each side by '-13'.
z = -0.6923076923

Simplifying
z = -0.6923076923