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

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


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

Reorder the terms:
10(2 + z) + -2(z + -2) = 3(z + -3) + 4(z + -4)
(2 * 10 + z * 10) + -2(z + -2) = 3(z + -3) + 4(z + -4)
(20 + 10z) + -2(z + -2) = 3(z + -3) + 4(z + -4)

Reorder the terms:
20 + 10z + -2(-2 + z) = 3(z + -3) + 4(z + -4)
20 + 10z + (-2 * -2 + z * -2) = 3(z + -3) + 4(z + -4)
20 + 10z + (4 + -2z) = 3(z + -3) + 4(z + -4)

Reorder the terms:
20 + 4 + 10z + -2z = 3(z + -3) + 4(z + -4)

Combine like terms: 20 + 4 = 24
24 + 10z + -2z = 3(z + -3) + 4(z + -4)

Combine like terms: 10z + -2z = 8z
24 + 8z = 3(z + -3) + 4(z + -4)

Reorder the terms:
24 + 8z = 3(-3 + z) + 4(z + -4)
24 + 8z = (-3 * 3 + z * 3) + 4(z + -4)
24 + 8z = (-9 + 3z) + 4(z + -4)

Reorder the terms:
24 + 8z = -9 + 3z + 4(-4 + z)
24 + 8z = -9 + 3z + (-4 * 4 + z * 4)
24 + 8z = -9 + 3z + (-16 + 4z)

Reorder the terms:
24 + 8z = -9 + -16 + 3z + 4z

Combine like terms: -9 + -16 = -25
24 + 8z = -25 + 3z + 4z

Combine like terms: 3z + 4z = 7z
24 + 8z = -25 + 7z

Solving
24 + 8z = -25 + 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.
24 + 8z + -7z = -25 + 7z + -7z

Combine like terms: 8z + -7z = 1z
24 + 1z = -25 + 7z + -7z

Combine like terms: 7z + -7z = 0
24 + 1z = -25 + 0
24 + 1z = -25

Add '-24' to each side of the equation.
24 + -24 + 1z = -25 + -24

Combine like terms: 24 + -24 = 0
0 + 1z = -25 + -24
1z = -25 + -24

Combine like terms: -25 + -24 = -49
1z = -49

Divide each side by '1'.
z = -49

Simplifying
z = -49

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