12⋅(z+1)+14⋅(z+3)=3-13⋅(z+2)

Simplify each term.

Apply the distributive property.

12z+12⋅1+14⋅(z+3)=3-13⋅(z+2)

Combine 12 and z.

z2+12⋅1+14⋅(z+3)=3-13⋅(z+2)

Multiply 12 by 1.

z2+12+14⋅(z+3)=3-13⋅(z+2)

Apply the distributive property.

z2+12+14z+14⋅3=3-13⋅(z+2)

Combine 14 and z.

z2+12+z4+14⋅3=3-13⋅(z+2)

Combine 14 and 3.

z2+12+z4+34=3-13⋅(z+2)

z2+12+z4+34=3-13⋅(z+2)

To write z2 as a fraction with a common denominator, multiply by 22.

z2⋅22+z4+12+34=3-13⋅(z+2)

Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.

Multiply z2 and 22.

z⋅22⋅2+z4+12+34=3-13⋅(z+2)

Multiply 2 by 2.

z⋅24+z4+12+34=3-13⋅(z+2)

z⋅24+z4+12+34=3-13⋅(z+2)

Combine the numerators over the common denominator.

z⋅2+z4+12+34=3-13⋅(z+2)

Add z⋅2 and z.

Reorder z and 2.

2⋅z+z4+12+34=3-13⋅(z+2)

Add 2⋅z and z.

3⋅z4+12+34=3-13⋅(z+2)

3⋅z4+12+34=3-13⋅(z+2)

To write 12 as a fraction with a common denominator, multiply by 22.

3z4+12⋅22+34=3-13⋅(z+2)

Write each expression with a common denominator of 4, by multiplying each by an appropriate factor of 1.

Multiply 12 and 22.

3z4+22⋅2+34=3-13⋅(z+2)

Multiply 2 by 2.

3z4+24+34=3-13⋅(z+2)

3z4+24+34=3-13⋅(z+2)

Combine the numerators over the common denominator.

3z4+2+34=3-13⋅(z+2)

Add 2 and 3.

3z4+54=3-13⋅(z+2)

3z4+54=3-13⋅(z+2)

Simplify each term.

Apply the distributive property.

3z4+54=3-13z-13⋅2

Combine z and 13.

3z4+54=3-z3-13⋅2

Multiply -13⋅2.

Multiply 2 by -1.

3z4+54=3-z3-2(13)

Combine -2 and 13.

3z4+54=3-z3+-23

3z4+54=3-z3+-23

Move the negative in front of the fraction.

3z4+54=3-z3-23

3z4+54=3-z3-23

To write 3 as a fraction with a common denominator, multiply by 33.

3z4+54=-z3+3⋅33-23

Combine 3 and 33.

3z4+54=-z3+3⋅33-23

Combine the numerators over the common denominator.

3z4+54=-z3+3⋅3-23

Simplify the numerator.

Multiply 3 by 3.

3z4+54=-z3+9-23

Subtract 2 from 9.

3z4+54=-z3+73

3z4+54=-z3+73

3z4+54=-z3+73

Add z3 to both sides of the equation.

3z4+54+z3=73

To write 3z4 as a fraction with a common denominator, multiply by 33.

3z4⋅33+z3+54=73

To write z3 as a fraction with a common denominator, multiply by 44.

3z4⋅33+z3⋅44+54=73

Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.

Multiply 3z4 and 33.

3z⋅34⋅3+z3⋅44+54=73

Multiply 4 by 3.

3z⋅312+z3⋅44+54=73

Multiply z3 and 44.

3z⋅312+z⋅43⋅4+54=73

Multiply 3 by 4.

3z⋅312+z⋅412+54=73

3z⋅312+z⋅412+54=73

Combine the numerators over the common denominator.

3z⋅3+z⋅412+54=73

Simplify each term.

Simplify the numerator.

Factor z out of 3z⋅3+z⋅4.

Factor z out of 3z⋅3.

z(3⋅3)+z⋅412+54=73

Factor z out of z⋅4.

z(3⋅3)+z(4)12+54=73

Factor z out of z(3⋅3)+z(4).

z(3⋅3+4)12+54=73

z(3⋅3+4)12+54=73

Multiply 3 by 3.

z(9+4)12+54=73

Add 9 and 4.

z⋅1312+54=73

z⋅1312+54=73

Move 13 to the left of z.

13z12+54=73

13z12+54=73

13z12+54=73

Subtract 54 from both sides of the equation.

13z12=73-54

To write 73 as a fraction with a common denominator, multiply by 44.

13z12=73⋅44-54

To write -54 as a fraction with a common denominator, multiply by 33.

13z12=73⋅44-54⋅33

Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.

Multiply 73 and 44.

13z12=7⋅43⋅4-54⋅33

Multiply 3 by 4.

13z12=7⋅412-54⋅33

Multiply 54 and 33.

13z12=7⋅412-5⋅34⋅3

Multiply 4 by 3.

13z12=7⋅412-5⋅312

13z12=7⋅412-5⋅312

Combine the numerators over the common denominator.

13z12=7⋅4-5⋅312

Simplify the numerator.

Multiply 7 by 4.

13z12=28-5⋅312

Multiply -5 by 3.

13z12=28-1512

Subtract 15 from 28.

13z12=1312

13z12=1312

13z12=1312

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

13z=13

Divide each term in 13z=13 by 13.

13z13=1313

Cancel the common factor of 13.

Cancel the common factor.

13z13=1313

Divide z by 1.

z=1313

z=1313

Divide 13 by 13.

z=1

z=1

Solve for z 1/2*(z+1)+1/4*(z+3)=3-1/3*(z+2)