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

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

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

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

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

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

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

Combine like terms: 10z + -4z = 6z
52 + 6z = 2(z + -3) + 3(z + -3)

Reorder the terms:
52 + 6z = 2(-3 + z) + 3(z + -3)
52 + 6z = (-3 * 2 + z * 2) + 3(z + -3)
52 + 6z = (-6 + 2z) + 3(z + -3)

Reorder the terms:
52 + 6z = -6 + 2z + 3(-3 + z)
52 + 6z = -6 + 2z + (-3 * 3 + z * 3)
52 + 6z = -6 + 2z + (-9 + 3z)

Reorder the terms:
52 + 6z = -6 + -9 + 2z + 3z

Combine like terms: -6 + -9 = -15
52 + 6z = -15 + 2z + 3z

Combine like terms: 2z + 3z = 5z
52 + 6z = -15 + 5z

Solving
52 + 6z = -15 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
52 + 6z + -5z = -15 + 5z + -5z

Combine like terms: 6z + -5z = 1z
52 + 1z = -15 + 5z + -5z

Combine like terms: 5z + -5z = 0
52 + 1z = -15 + 0
52 + 1z = -15

Add '-52' to each side of the equation.
52 + -52 + 1z = -15 + -52

Combine like terms: 52 + -52 = 0
0 + 1z = -15 + -52
1z = -15 + -52

Combine like terms: -15 + -52 = -67
1z = -67

Divide each side by '1'.
z = -67

Simplifying
z = -67