3[5z-7]-2[9z-11]=41[8z-13]-17

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Solution for 3[5z-7]-2[9z-11]=41[8z-13]-17 equation: 


Simplifying
3[5z + -7] + -2[9z + -11] = 41[8z + -13] + -17

Reorder the terms:
3[-7 + 5z] + -2[9z + -11] = 41[8z + -13] + -17
[-7 * 3 + 5z * 3] + -2[9z + -11] = 41[8z + -13] + -17
[-21 + 15z] + -2[9z + -11] = 41[8z + -13] + -17

Reorder the terms:
-21 + 15z + -2[-11 + 9z] = 41[8z + -13] + -17
-21 + 15z + [-11 * -2 + 9z * -2] = 41[8z + -13] + -17
-21 + 15z + [22 + -18z] = 41[8z + -13] + -17

Reorder the terms:
-21 + 22 + 15z + -18z = 41[8z + -13] + -17

Combine like terms: -21 + 22 = 1
1 + 15z + -18z = 41[8z + -13] + -17

Combine like terms: 15z + -18z = -3z
1 + -3z = 41[8z + -13] + -17

Reorder the terms:
1 + -3z = 41[-13 + 8z] + -17
1 + -3z = [-13 * 41 + 8z * 41] + -17
1 + -3z = [-533 + 328z] + -17

Reorder the terms:
1 + -3z = -533 + -17 + 328z

Combine like terms: -533 + -17 = -550
1 + -3z = -550 + 328z

Solving
1 + -3z = -550 + 328z

Solving for variable 'z'.

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

Add '-328z' to each side of the equation.
1 + -3z + -328z = -550 + 328z + -328z

Combine like terms: -3z + -328z = -331z
1 + -331z = -550 + 328z + -328z

Combine like terms: 328z + -328z = 0
1 + -331z = -550 + 0
1 + -331z = -550

Add '-1' to each side of the equation.
1 + -1 + -331z = -550 + -1

Combine like terms: 1 + -1 = 0
0 + -331z = -550 + -1
-331z = -550 + -1

Combine like terms: -550 + -1 = -551
-331z = -551

Divide each side by '-331'.
z = 1.664652568

Simplifying
z = 1.664652568

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