10z-6(3z+4)=5(2z+(3z+4)-22)

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Solution for 10z-6(3z+4)=5(2z+(3z+4)-22) equation:


Simplifying
10z + -6(3z + 4) = 5(2z + (3z + 4) + -22)

Reorder the terms:
10z + -6(4 + 3z) = 5(2z + (3z + 4) + -22)
10z + (4 * -6 + 3z * -6) = 5(2z + (3z + 4) + -22)
10z + (-24 + -18z) = 5(2z + (3z + 4) + -22)

Reorder the terms:
-24 + 10z + -18z = 5(2z + (3z + 4) + -22)

Combine like terms: 10z + -18z = -8z
-24 + -8z = 5(2z + (3z + 4) + -22)

Reorder the terms:
-24 + -8z = 5(2z + (4 + 3z) + -22)

Remove parenthesis around (4 + 3z)
-24 + -8z = 5(2z + 4 + 3z + -22)

Reorder the terms:
-24 + -8z = 5(4 + -22 + 2z + 3z)

Combine like terms: 4 + -22 = -18
-24 + -8z = 5(-18 + 2z + 3z)

Combine like terms: 2z + 3z = 5z
-24 + -8z = 5(-18 + 5z)
-24 + -8z = (-18 * 5 + 5z * 5)
-24 + -8z = (-90 + 25z)

Solving
-24 + -8z = -90 + 25z

Solving for variable 'z'.

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

Add '-25z' to each side of the equation.
-24 + -8z + -25z = -90 + 25z + -25z

Combine like terms: -8z + -25z = -33z
-24 + -33z = -90 + 25z + -25z

Combine like terms: 25z + -25z = 0
-24 + -33z = -90 + 0
-24 + -33z = -90

Add '24' to each side of the equation.
-24 + 24 + -33z = -90 + 24

Combine like terms: -24 + 24 = 0
0 + -33z = -90 + 24
-33z = -90 + 24

Combine like terms: -90 + 24 = -66
-33z = -66

Divide each side by '-33'.
z = 2

Simplifying
z = 2

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