7y+3(z-6)=5(y+2)-5

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Solution for 7y+3(z-6)=5(y+2)-5 equation:


Simplifying
7y + 3(z + -6) = 5(y + 2) + -5

Reorder the terms:
7y + 3(-6 + z) = 5(y + 2) + -5
7y + (-6 * 3 + z * 3) = 5(y + 2) + -5
7y + (-18 + 3z) = 5(y + 2) + -5

Reorder the terms:
-18 + 7y + 3z = 5(y + 2) + -5

Reorder the terms:
-18 + 7y + 3z = 5(2 + y) + -5
-18 + 7y + 3z = (2 * 5 + y * 5) + -5
-18 + 7y + 3z = (10 + 5y) + -5

Reorder the terms:
-18 + 7y + 3z = 10 + -5 + 5y

Combine like terms: 10 + -5 = 5
-18 + 7y + 3z = 5 + 5y

Solving
-18 + 7y + 3z = 5 + 5y

Solving for variable 'y'.

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

Add '-5y' to each side of the equation.
-18 + 7y + -5y + 3z = 5 + 5y + -5y

Combine like terms: 7y + -5y = 2y
-18 + 2y + 3z = 5 + 5y + -5y

Combine like terms: 5y + -5y = 0
-18 + 2y + 3z = 5 + 0
-18 + 2y + 3z = 5

Add '18' to each side of the equation.
-18 + 2y + 18 + 3z = 5 + 18

Reorder the terms:
-18 + 18 + 2y + 3z = 5 + 18

Combine like terms: -18 + 18 = 0
0 + 2y + 3z = 5 + 18
2y + 3z = 5 + 18

Combine like terms: 5 + 18 = 23
2y + 3z = 23

Add '-3z' to each side of the equation.
2y + 3z + -3z = 23 + -3z

Combine like terms: 3z + -3z = 0
2y + 0 = 23 + -3z
2y = 23 + -3z

Divide each side by '2'.
y = 11.5 + -1.5z

Simplifying
y = 11.5 + -1.5z

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