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

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Solution for 10(z+1)-4(z-2)=3(z-3)+2(z-4) equation:


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

Reorder the terms:
10(1 + z) + -4(z + -2) = 3(z + -3) + 2(z + -4)
(1 * 10 + z * 10) + -4(z + -2) = 3(z + -3) + 2(z + -4)
(10 + 10z) + -4(z + -2) = 3(z + -3) + 2(z + -4)

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

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

Combine like terms: 10 + 8 = 18
18 + 10z + -4z = 3(z + -3) + 2(z + -4)

Combine like terms: 10z + -4z = 6z
18 + 6z = 3(z + -3) + 2(z + -4)

Reorder the terms:
18 + 6z = 3(-3 + z) + 2(z + -4)
18 + 6z = (-3 * 3 + z * 3) + 2(z + -4)
18 + 6z = (-9 + 3z) + 2(z + -4)

Reorder the terms:
18 + 6z = -9 + 3z + 2(-4 + z)
18 + 6z = -9 + 3z + (-4 * 2 + z * 2)
18 + 6z = -9 + 3z + (-8 + 2z)

Reorder the terms:
18 + 6z = -9 + -8 + 3z + 2z

Combine like terms: -9 + -8 = -17
18 + 6z = -17 + 3z + 2z

Combine like terms: 3z + 2z = 5z
18 + 6z = -17 + 5z

Solving
18 + 6z = -17 + 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.
18 + 6z + -5z = -17 + 5z + -5z

Combine like terms: 6z + -5z = 1z
18 + 1z = -17 + 5z + -5z

Combine like terms: 5z + -5z = 0
18 + 1z = -17 + 0
18 + 1z = -17

Add '-18' to each side of the equation.
18 + -18 + 1z = -17 + -18

Combine like terms: 18 + -18 = 0
0 + 1z = -17 + -18
1z = -17 + -18

Combine like terms: -17 + -18 = -35
1z = -35

Divide each side by '1'.
z = -35

Simplifying
z = -35

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