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

Solution for 10(z+4)-4(z-2)=2(z-2)+3(z-3) equation:

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

Reorder the terms:
10(4 + z) + -4(z + -2) = 2(z + -2) + 3(z + -3)
(4 * 10 + z * 10) + -4(z + -2) = 2(z + -2) + 3(z + -3)
(40 + 10z) + -4(z + -2) = 2(z + -2) + 3(z + -3)

Reorder the terms:
40 + 10z + -4(-2 + z) = 2(z + -2) + 3(z + -3)
40 + 10z + (-2 * -4 + z * -4) = 2(z + -2) + 3(z + -3)
40 + 10z + (8 + -4z) = 2(z + -2) + 3(z + -3)

Reorder the terms:
40 + 8 + 10z + -4z = 2(z + -2) + 3(z + -3)

Combine like terms: 40 + 8 = 48
48 + 10z + -4z = 2(z + -2) + 3(z + -3)

Combine like terms: 10z + -4z = 6z
48 + 6z = 2(z + -2) + 3(z + -3)

Reorder the terms:
48 + 6z = 2(-2 + z) + 3(z + -3)
48 + 6z = (-2 * 2 + z * 2) + 3(z + -3)
48 + 6z = (-4 + 2z) + 3(z + -3)

Reorder the terms:
48 + 6z = -4 + 2z + 3(-3 + z)
48 + 6z = -4 + 2z + (-3 * 3 + z * 3)
48 + 6z = -4 + 2z + (-9 + 3z)

Reorder the terms:
48 + 6z = -4 + -9 + 2z + 3z

Combine like terms: -4 + -9 = -13
48 + 6z = -13 + 2z + 3z

Combine like terms: 2z + 3z = 5z
48 + 6z = -13 + 5z

Solving
48 + 6z = -13 + 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.
48 + 6z + -5z = -13 + 5z + -5z

Combine like terms: 6z + -5z = 1z
48 + 1z = -13 + 5z + -5z

Combine like terms: 5z + -5z = 0
48 + 1z = -13 + 0
48 + 1z = -13

Add '-48' to each side of the equation.
48 + -48 + 1z = -13 + -48

Combine like terms: 48 + -48 = 0
0 + 1z = -13 + -48
1z = -13 + -48

Combine like terms: -13 + -48 = -61
1z = -61

Divide each side by '1'.
z = -61

Simplifying
z = -61