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

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

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

Reorder the terms:
7(4 + z) + -2(z + -3) = 2(z + -3) + 2(z + -4)
(4 * 7 + z * 7) + -2(z + -3) = 2(z + -3) + 2(z + -4)
(28 + 7z) + -2(z + -3) = 2(z + -3) + 2(z + -4)

Reorder the terms:
28 + 7z + -2(-3 + z) = 2(z + -3) + 2(z + -4)
28 + 7z + (-3 * -2 + z * -2) = 2(z + -3) + 2(z + -4)
28 + 7z + (6 + -2z) = 2(z + -3) + 2(z + -4)

Reorder the terms:
28 + 6 + 7z + -2z = 2(z + -3) + 2(z + -4)

Combine like terms: 28 + 6 = 34
34 + 7z + -2z = 2(z + -3) + 2(z + -4)

Combine like terms: 7z + -2z = 5z
34 + 5z = 2(z + -3) + 2(z + -4)

Reorder the terms:
34 + 5z = 2(-3 + z) + 2(z + -4)
34 + 5z = (-3 * 2 + z * 2) + 2(z + -4)
34 + 5z = (-6 + 2z) + 2(z + -4)

Reorder the terms:
34 + 5z = -6 + 2z + 2(-4 + z)
34 + 5z = -6 + 2z + (-4 * 2 + z * 2)
34 + 5z = -6 + 2z + (-8 + 2z)

Reorder the terms:
34 + 5z = -6 + -8 + 2z + 2z

Combine like terms: -6 + -8 = -14
34 + 5z = -14 + 2z + 2z

Combine like terms: 2z + 2z = 4z
34 + 5z = -14 + 4z

Solving
34 + 5z = -14 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
34 + 5z + -4z = -14 + 4z + -4z

Combine like terms: 5z + -4z = 1z
34 + 1z = -14 + 4z + -4z

Combine like terms: 4z + -4z = 0
34 + 1z = -14 + 0
34 + 1z = -14

Add '-34' to each side of the equation.
34 + -34 + 1z = -14 + -34

Combine like terms: 34 + -34 = 0
0 + 1z = -14 + -34
1z = -14 + -34

Combine like terms: -14 + -34 = -48
1z = -48

Divide each side by '1'.
z = -48

Simplifying
z = -48