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

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


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

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

Reorder the terms:
10 + 10z + -3(-4 + z) = 3(z + -2) + 3(z + -4)
10 + 10z + (-4 * -3 + z * -3) = 3(z + -2) + 3(z + -4)
10 + 10z + (12 + -3z) = 3(z + -2) + 3(z + -4)

Reorder the terms:
10 + 12 + 10z + -3z = 3(z + -2) + 3(z + -4)

Combine like terms: 10 + 12 = 22
22 + 10z + -3z = 3(z + -2) + 3(z + -4)

Combine like terms: 10z + -3z = 7z
22 + 7z = 3(z + -2) + 3(z + -4)

Reorder the terms:
22 + 7z = 3(-2 + z) + 3(z + -4)
22 + 7z = (-2 * 3 + z * 3) + 3(z + -4)
22 + 7z = (-6 + 3z) + 3(z + -4)

Reorder the terms:
22 + 7z = -6 + 3z + 3(-4 + z)
22 + 7z = -6 + 3z + (-4 * 3 + z * 3)
22 + 7z = -6 + 3z + (-12 + 3z)

Reorder the terms:
22 + 7z = -6 + -12 + 3z + 3z

Combine like terms: -6 + -12 = -18
22 + 7z = -18 + 3z + 3z

Combine like terms: 3z + 3z = 6z
22 + 7z = -18 + 6z

Solving
22 + 7z = -18 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
22 + 7z + -6z = -18 + 6z + -6z

Combine like terms: 7z + -6z = 1z
22 + 1z = -18 + 6z + -6z

Combine like terms: 6z + -6z = 0
22 + 1z = -18 + 0
22 + 1z = -18

Add '-22' to each side of the equation.
22 + -22 + 1z = -18 + -22

Combine like terms: 22 + -22 = 0
0 + 1z = -18 + -22
1z = -18 + -22

Combine like terms: -18 + -22 = -40
1z = -40

Divide each side by '1'.
z = -40

Simplifying
z = -40

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