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

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


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

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

Reorder the terms:
20 + 10z + -3(-3 + z) = 4(z + -2) + 2(z + -4)
20 + 10z + (-3 * -3 + z * -3) = 4(z + -2) + 2(z + -4)
20 + 10z + (9 + -3z) = 4(z + -2) + 2(z + -4)

Reorder the terms:
20 + 9 + 10z + -3z = 4(z + -2) + 2(z + -4)

Combine like terms: 20 + 9 = 29
29 + 10z + -3z = 4(z + -2) + 2(z + -4)

Combine like terms: 10z + -3z = 7z
29 + 7z = 4(z + -2) + 2(z + -4)

Reorder the terms:
29 + 7z = 4(-2 + z) + 2(z + -4)
29 + 7z = (-2 * 4 + z * 4) + 2(z + -4)
29 + 7z = (-8 + 4z) + 2(z + -4)

Reorder the terms:
29 + 7z = -8 + 4z + 2(-4 + z)
29 + 7z = -8 + 4z + (-4 * 2 + z * 2)
29 + 7z = -8 + 4z + (-8 + 2z)

Reorder the terms:
29 + 7z = -8 + -8 + 4z + 2z

Combine like terms: -8 + -8 = -16
29 + 7z = -16 + 4z + 2z

Combine like terms: 4z + 2z = 6z
29 + 7z = -16 + 6z

Solving
29 + 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.
29 + 7z + -6z = -16 + 6z + -6z

Combine like terms: 7z + -6z = 1z
29 + 1z = -16 + 6z + -6z

Combine like terms: 6z + -6z = 0
29 + 1z = -16 + 0
29 + 1z = -16

Add '-29' to each side of the equation.
29 + -29 + 1z = -16 + -29

Combine like terms: 29 + -29 = 0
0 + 1z = -16 + -29
1z = -16 + -29

Combine like terms: -16 + -29 = -45
1z = -45

Divide each side by '1'.
z = -45

Simplifying
z = -45

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