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

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


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

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

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

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

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

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

Reorder the terms:
-24 + -8z = 5[4 + -22 + 3x + 2z]

Combine like terms: 4 + -22 = -18
-24 + -8z = 5[-18 + 3x + 2z]
-24 + -8z = [-18 * 5 + 3x * 5 + 2z * 5]
-24 + -8z = [-90 + 15x + 10z]

Solving
-24 + -8z = -90 + 15x + 10z

Solving for variable 'z'.

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

Add '-10z' to each side of the equation.
-24 + -8z + -10z = -90 + 15x + 10z + -10z

Combine like terms: -8z + -10z = -18z
-24 + -18z = -90 + 15x + 10z + -10z

Combine like terms: 10z + -10z = 0
-24 + -18z = -90 + 15x + 0
-24 + -18z = -90 + 15x

Add '24' to each side of the equation.
-24 + 24 + -18z = -90 + 24 + 15x

Combine like terms: -24 + 24 = 0
0 + -18z = -90 + 24 + 15x
-18z = -90 + 24 + 15x

Combine like terms: -90 + 24 = -66
-18z = -66 + 15x

Divide each side by '-18'.
z = 3.666666667 + -0.8333333333x

Simplifying
z = 3.666666667 + -0.8333333333x

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