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

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

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

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

Reorder the terms:
40 + 10z + -3(-3 + z) = 4(z + -3z) + 2(z + -3)
40 + 10z + (-3 * -3 + z * -3) = 4(z + -3z) + 2(z + -3)
40 + 10z + (9 + -3z) = 4(z + -3z) + 2(z + -3)

Reorder the terms:
40 + 9 + 10z + -3z = 4(z + -3z) + 2(z + -3)

Combine like terms: 40 + 9 = 49
49 + 10z + -3z = 4(z + -3z) + 2(z + -3)

Combine like terms: 10z + -3z = 7z
49 + 7z = 4(z + -3z) + 2(z + -3)

Combine like terms: z + -3z = -2z
49 + 7z = 4(-2z) + 2(z + -3)

Remove parenthesis around (-2z)
49 + 7z = 4 * -2z + 2(z + -3)

Multiply 4 * -2
49 + 7z = -8z + 2(z + -3)

Reorder the terms:
49 + 7z = -8z + 2(-3 + z)
49 + 7z = -8z + (-3 * 2 + z * 2)
49 + 7z = -8z + (-6 + 2z)

Reorder the terms:
49 + 7z = -6 + -8z + 2z

Combine like terms: -8z + 2z = -6z
49 + 7z = -6 + -6z

Solving
49 + 7z = -6 + -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.
49 + 7z + 6z = -6 + -6z + 6z

Combine like terms: 7z + 6z = 13z
49 + 13z = -6 + -6z + 6z

Combine like terms: -6z + 6z = 0
49 + 13z = -6 + 0
49 + 13z = -6

Add '-49' to each side of the equation.
49 + -49 + 13z = -6 + -49

Combine like terms: 49 + -49 = 0
0 + 13z = -6 + -49
13z = -6 + -49

Combine like terms: -6 + -49 = -55
13z = -55

Divide each side by '13'.
z = -4.230769231

Simplifying
z = -4.230769231