5z(z-2)-3(2z-1)=5z(z-3)+7

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Solution for 5z(z-2)-3(2z-1)=5z(z-3)+7 equation: 


Simplifying
5z(z + -2) + -3(2z + -1) = 5z(z + -3) + 7

Reorder the terms:
5z(-2 + z) + -3(2z + -1) = 5z(z + -3) + 7
(-2 * 5z + z * 5z) + -3(2z + -1) = 5z(z + -3) + 7
(-10z + 5z2) + -3(2z + -1) = 5z(z + -3) + 7

Reorder the terms:
-10z + 5z2 + -3(-1 + 2z) = 5z(z + -3) + 7
-10z + 5z2 + (-1 * -3 + 2z * -3) = 5z(z + -3) + 7
-10z + 5z2 + (3 + -6z) = 5z(z + -3) + 7

Reorder the terms:
3 + -10z + -6z + 5z2 = 5z(z + -3) + 7

Combine like terms: -10z + -6z = -16z
3 + -16z + 5z2 = 5z(z + -3) + 7

Reorder the terms:
3 + -16z + 5z2 = 5z(-3 + z) + 7
3 + -16z + 5z2 = (-3 * 5z + z * 5z) + 7
3 + -16z + 5z2 = (-15z + 5z2) + 7

Reorder the terms:
3 + -16z + 5z2 = 7 + -15z + 5z2

Add '-5z2' to each side of the equation.
3 + -16z + 5z2 + -5z2 = 7 + -15z + 5z2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
3 + -16z + 0 = 7 + -15z + 5z2 + -5z2
3 + -16z = 7 + -15z + 5z2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
3 + -16z = 7 + -15z + 0
3 + -16z = 7 + -15z

Solving
3 + -16z = 7 + -15z

Solving for variable 'z'.

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

Add '15z' to each side of the equation.
3 + -16z + 15z = 7 + -15z + 15z

Combine like terms: -16z + 15z = -1z
3 + -1z = 7 + -15z + 15z

Combine like terms: -15z + 15z = 0
3 + -1z = 7 + 0
3 + -1z = 7

Add '-3' to each side of the equation.
3 + -3 + -1z = 7 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 7 + -3
-1z = 7 + -3

Combine like terms: 7 + -3 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4

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