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

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


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

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

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

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

Combine like terms: 10 + 4 = 14
14 + 10z + -2z = 3(z + -2) + 4(z + -3)

Combine like terms: 10z + -2z = 8z
14 + 8z = 3(z + -2) + 4(z + -3)

Reorder the terms:
14 + 8z = 3(-2 + z) + 4(z + -3)
14 + 8z = (-2 * 3 + z * 3) + 4(z + -3)
14 + 8z = (-6 + 3z) + 4(z + -3)

Reorder the terms:
14 + 8z = -6 + 3z + 4(-3 + z)
14 + 8z = -6 + 3z + (-3 * 4 + z * 4)
14 + 8z = -6 + 3z + (-12 + 4z)

Reorder the terms:
14 + 8z = -6 + -12 + 3z + 4z

Combine like terms: -6 + -12 = -18
14 + 8z = -18 + 3z + 4z

Combine like terms: 3z + 4z = 7z
14 + 8z = -18 + 7z

Solving
14 + 8z = -18 + 7z

Solving for variable 'z'.

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

Add '-7z' to each side of the equation.
14 + 8z + -7z = -18 + 7z + -7z

Combine like terms: 8z + -7z = 1z
14 + 1z = -18 + 7z + -7z

Combine like terms: 7z + -7z = 0
14 + 1z = -18 + 0
14 + 1z = -18

Add '-14' to each side of the equation.
14 + -14 + 1z = -18 + -14

Combine like terms: 14 + -14 = 0
0 + 1z = -18 + -14
1z = -18 + -14

Combine like terms: -18 + -14 = -32
1z = -32

Divide each side by '1'.
z = -32

Simplifying
z = -32

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