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

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


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

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

Reorder the terms:
40 + 10z + -3(-4 + z) = 2(z + -2) + 4(z + -3)
40 + 10z + (-4 * -3 + z * -3) = 2(z + -2) + 4(z + -3)
40 + 10z + (12 + -3z) = 2(z + -2) + 4(z + -3)

Reorder the terms:
40 + 12 + 10z + -3z = 2(z + -2) + 4(z + -3)

Combine like terms: 40 + 12 = 52
52 + 10z + -3z = 2(z + -2) + 4(z + -3)

Combine like terms: 10z + -3z = 7z
52 + 7z = 2(z + -2) + 4(z + -3)

Reorder the terms:
52 + 7z = 2(-2 + z) + 4(z + -3)
52 + 7z = (-2 * 2 + z * 2) + 4(z + -3)
52 + 7z = (-4 + 2z) + 4(z + -3)

Reorder the terms:
52 + 7z = -4 + 2z + 4(-3 + z)
52 + 7z = -4 + 2z + (-3 * 4 + z * 4)
52 + 7z = -4 + 2z + (-12 + 4z)

Reorder the terms:
52 + 7z = -4 + -12 + 2z + 4z

Combine like terms: -4 + -12 = -16
52 + 7z = -16 + 2z + 4z

Combine like terms: 2z + 4z = 6z
52 + 7z = -16 + 6z

Solving
52 + 7z = -16 + 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.
52 + 7z + -6z = -16 + 6z + -6z

Combine like terms: 7z + -6z = 1z
52 + 1z = -16 + 6z + -6z

Combine like terms: 6z + -6z = 0
52 + 1z = -16 + 0
52 + 1z = -16

Add '-52' to each side of the equation.
52 + -52 + 1z = -16 + -52

Combine like terms: 52 + -52 = 0
0 + 1z = -16 + -52
1z = -16 + -52

Combine like terms: -16 + -52 = -68
1z = -68

Divide each side by '1'.
z = -68

Simplifying
z = -68

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