100(z+4)-4(z-2)=3(z-1)+2(z-3)

Solution for 100(z+4)-4(z-2)=3(z-1)+2(z-3) equation:

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

Reorder the terms:
100(4 + z) + -4(z + -2) = 3(z + -1) + 2(z + -3)
(4 * 100 + z * 100) + -4(z + -2) = 3(z + -1) + 2(z + -3)
(400 + 100z) + -4(z + -2) = 3(z + -1) + 2(z + -3)

Reorder the terms:
400 + 100z + -4(-2 + z) = 3(z + -1) + 2(z + -3)
400 + 100z + (-2 * -4 + z * -4) = 3(z + -1) + 2(z + -3)
400 + 100z + (8 + -4z) = 3(z + -1) + 2(z + -3)

Reorder the terms:
400 + 8 + 100z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: 400 + 8 = 408
408 + 100z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: 100z + -4z = 96z
408 + 96z = 3(z + -1) + 2(z + -3)

Reorder the terms:
408 + 96z = 3(-1 + z) + 2(z + -3)
408 + 96z = (-1 * 3 + z * 3) + 2(z + -3)
408 + 96z = (-3 + 3z) + 2(z + -3)

Reorder the terms:
408 + 96z = -3 + 3z + 2(-3 + z)
408 + 96z = -3 + 3z + (-3 * 2 + z * 2)
408 + 96z = -3 + 3z + (-6 + 2z)

Reorder the terms:
408 + 96z = -3 + -6 + 3z + 2z

Combine like terms: -3 + -6 = -9
408 + 96z = -9 + 3z + 2z

Combine like terms: 3z + 2z = 5z
408 + 96z = -9 + 5z

Solving
408 + 96z = -9 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
408 + 96z + -5z = -9 + 5z + -5z

Combine like terms: 96z + -5z = 91z
408 + 91z = -9 + 5z + -5z

Combine like terms: 5z + -5z = 0
408 + 91z = -9 + 0
408 + 91z = -9

Add '-408' to each side of the equation.
408 + -408 + 91z = -9 + -408

Combine like terms: 408 + -408 = 0
0 + 91z = -9 + -408
91z = -9 + -408

Combine like terms: -9 + -408 = -417
91z = -417

Divide each side by '91'.
z = -4.582417582

Simplifying
z = -4.582417582