z+3.5z+5.2=6.8(z+5.5)

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Solution for z+3.5z+5.2=6.8(z+5.5) equation:


Simplifying
z + 3.5z + 5.2 = 6.8(z + 5.5)

Reorder the terms:
5.2 + z + 3.5z = 6.8(z + 5.5)

Combine like terms: z + 3.5z = 4.5z
5.2 + 4.5z = 6.8(z + 5.5)

Reorder the terms:
5.2 + 4.5z = 6.8(5.5 + z)
5.2 + 4.5z = (5.5 * 6.8 + z * 6.8)
5.2 + 4.5z = (37.4 + 6.8z)

Solving
5.2 + 4.5z = 37.4 + 6.8z

Solving for variable 'z'.

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

Add '-6.8z' to each side of the equation.
5.2 + 4.5z + -6.8z = 37.4 + 6.8z + -6.8z

Combine like terms: 4.5z + -6.8z = -2.3z
5.2 + -2.3z = 37.4 + 6.8z + -6.8z

Combine like terms: 6.8z + -6.8z = 0.0
5.2 + -2.3z = 37.4 + 0.0
5.2 + -2.3z = 37.4

Add '-5.2' to each side of the equation.
5.2 + -5.2 + -2.3z = 37.4 + -5.2

Combine like terms: 5.2 + -5.2 = 0.0
0.0 + -2.3z = 37.4 + -5.2
-2.3z = 37.4 + -5.2

Combine like terms: 37.4 + -5.2 = 32.2
-2.3z = 32.2

Divide each side by '-2.3'.
z = -14

Simplifying
z = -14

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