3(4z-1)-4(z+3)=5(z+1)

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Solution for 3(4z-1)-4(z+3)=5(z+1) equation:


Simplifying
3(4z + -1) + -4(z + 3) = 5(z + 1)

Reorder the terms:
3(-1 + 4z) + -4(z + 3) = 5(z + 1)
(-1 * 3 + 4z * 3) + -4(z + 3) = 5(z + 1)
(-3 + 12z) + -4(z + 3) = 5(z + 1)

Reorder the terms:
-3 + 12z + -4(3 + z) = 5(z + 1)
-3 + 12z + (3 * -4 + z * -4) = 5(z + 1)
-3 + 12z + (-12 + -4z) = 5(z + 1)

Reorder the terms:
-3 + -12 + 12z + -4z = 5(z + 1)

Combine like terms: -3 + -12 = -15
-15 + 12z + -4z = 5(z + 1)

Combine like terms: 12z + -4z = 8z
-15 + 8z = 5(z + 1)

Reorder the terms:
-15 + 8z = 5(1 + z)
-15 + 8z = (1 * 5 + z * 5)
-15 + 8z = (5 + 5z)

Solving
-15 + 8z = 5 + 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.
-15 + 8z + -5z = 5 + 5z + -5z

Combine like terms: 8z + -5z = 3z
-15 + 3z = 5 + 5z + -5z

Combine like terms: 5z + -5z = 0
-15 + 3z = 5 + 0
-15 + 3z = 5

Add '15' to each side of the equation.
-15 + 15 + 3z = 5 + 15

Combine like terms: -15 + 15 = 0
0 + 3z = 5 + 15
3z = 5 + 15

Combine like terms: 5 + 15 = 20
3z = 20

Divide each side by '3'.
z = 6.666666667

Simplifying
z = 6.666666667

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