# Solve for z (z-3)/5+2=(z+2)/3-1

z-35+2=z+23-1
Simplify z-35+2.
To write 2 as a fraction with a common denominator, multiply by 55.
z-35+2⋅55=z+23-1
Simplify terms.
Combine 2 and 55.
z-35+2⋅55=z+23-1
Combine the numerators over the common denominator.
z-3+2⋅55=z+23-1
z-3+2⋅55=z+23-1
Simplify the numerator.
Multiply 2 by 5.
z-3+105=z+23-1
Add -3 and 10.
z+75=z+23-1
z+75=z+23-1
z+75=z+23-1
Simplify z+23-1.
To write -1 as a fraction with a common denominator, multiply by 33.
z+75=z+23-1⋅33
Simplify terms.
Combine -1 and 33.
z+75=z+23+-1⋅33
Combine the numerators over the common denominator.
z+75=z+2-1⋅33
z+75=z+2-1⋅33
Simplify the numerator.
Multiply -1 by 3.
z+75=z+2-33
Subtract 3 from 2.
z+75=z-13
z+75=z-13
z+75=z-13
Move all terms containing z to the left side of the equation.
Subtract z-13 from both sides of the equation.
z+75-z-13=0
To write z+75 as a fraction with a common denominator, multiply by 33.
z+75⋅33-z-13=0
To write -z-13 as a fraction with a common denominator, multiply by 55.
z+75⋅33-z-13⋅55=0
Write each expression with a common denominator of 15, by multiplying each by an appropriate factor of 1.
Multiply z+75 and 33.
(z+7)⋅35⋅3-z-13⋅55=0
Multiply 5 by 3.
(z+7)⋅315-z-13⋅55=0
Multiply z-13 and 55.
(z+7)⋅315-(z-1)⋅53⋅5=0
Multiply 3 by 5.
(z+7)⋅315-(z-1)⋅515=0
(z+7)⋅315-(z-1)⋅515=0
Combine the numerators over the common denominator.
(z+7)⋅3-(z-1)⋅515=0
Simplify the numerator.
Apply the distributive property.
z⋅3+7⋅3-(z-1)⋅515=0
Move 3 to the left of z.
3⋅z+7⋅3-(z-1)⋅515=0
Multiply 7 by 3.
3⋅z+21-(z-1)⋅515=0
Apply the distributive property.
3z+21+(-z–1)⋅515=0
Multiply -1 by -1.
3z+21+(-z+1)⋅515=0
Apply the distributive property.
3z+21-z⋅5+1⋅515=0
Multiply 5 by -1.
3z+21-5z+1⋅515=0
Multiply 5 by 1.
3z+21-5z+515=0
Subtract 5z from 3z.
-2z+21+515=0
Add 21 and 5.
-2z+2615=0
Factor 2 out of -2z+26.
Factor 2 out of -2z.
2(-z)+2615=0
Factor 2 out of 26.
2(-z)+2(13)15=0
Factor 2 out of 2(-z)+2(13).
2(-z+13)15=0
2(-z+13)15=0
2(-z+13)15=0
Factor -1 out of -z.
2(-(z)+13)15=0
Rewrite 13 as -1(-13).
2(-(z)-1(-13))15=0
Factor -1 out of -(z)-1(-13).
2(-(z-13))15=0
Rewrite -(z-13) as -1(z-13).
2(-1(z-13))15=0
Move the negative in front of the fraction.
-2(z-13)15=0
-2(z-13)15=0
Multiply both sides of the equation by -152.
-152⋅(-2(z-13)15)=-152⋅0
Simplify both sides of the equation.
Simplify -152⋅(-2(z-13)15).
Cancel the common factor of 15.
Move the leading negative in -152 into the numerator.
-152⋅(-2(z-13)15)=-152⋅0
Move the leading negative in -2(z-13)15 into the numerator.
-152⋅-2(z-13)15=-152⋅0
Factor 15 out of -15.
15(-1)2⋅-2(z-13)15=-152⋅0
Cancel the common factor.
15⋅-12⋅-2(z-13)15=-152⋅0
Rewrite the expression.
-12⋅(-2(z-13))=-152⋅0
-12⋅(-2(z-13))=-152⋅0
Cancel the common factor of 2.
Factor 2 out of -2(z-13).
-12⋅(2(-(z-13)))=-152⋅0
Cancel the common factor.
-12⋅(2(-(z-13)))=-152⋅0
Rewrite the expression.
-1⋅(-(z-13))=-152⋅0
-1⋅(-(z-13))=-152⋅0
Multiply.
Multiply -1 by -1.
1⋅(z-13)=-152⋅0
Multiply z-13 by 1.
z-13=-152⋅0
z-13=-152⋅0
z-13=-152⋅0
Multiply -152⋅0.
Multiply 0 by -1.
z-13=0(152)
Multiply 0 by 152.
z-13=0
z-13=0
z-13=0
Add 13 to both sides of the equation.
z=13
Solve for z (z-3)/5+2=(z+2)/3-1

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