12z+2(34z-1)=14z+6

Simplify each term.

Combine 12 and z.

z2+2(34z-1)=14z+6

Combine 34 and z.

z2+2(3z4-1)=14z+6

Apply the distributive property.

z2+23z4+2⋅-1=14z+6

Cancel the common factor of 2.

Factor 2 out of 4.

z2+23z2(2)+2⋅-1=14z+6

Cancel the common factor.

z2+23z2⋅2+2⋅-1=14z+6

Rewrite the expression.

z2+3z2+2⋅-1=14z+6

z2+3z2+2⋅-1=14z+6

Multiply 2 by -1.

z2+3z2-2=14z+6

z2+3z2-2=14z+6

Simplify terms.

Combine fractions with similar denominators.

-2+z+3z2=14z+6

Add z and 3z.

-2+4z2=14z+6

Reduce the expression 4z2 by cancelling the common factors.

Factor 2 out of 4z.

-2+2(2z)2=14z+6

Factor 2 out of 2.

-2+2(2z)2(1)=14z+6

Cancel the common factor.

-2+2(2z)2⋅1=14z+6

Rewrite the expression.

-2+2z1=14z+6

-2+2z1=14z+6

Divide 2z by 1.

-2+2z=14z+6

-2+2z=14z+6

-2+2z=14z+6

Combine 14 and z.

-2+2z=z4+6

Subtract z4 from both sides of the equation.

-2+2z-z4=6

To write 2z as a fraction with a common denominator, multiply by 44.

-2+2z⋅44-z4=6

Combine 2z and 44.

-2+2z⋅44-z4=6

Combine the numerators over the common denominator.

-2+2z⋅4-z4=6

Simplify each term.

Simplify the numerator.

Factor z out of 2z⋅4-z.

Factor z out of 2z⋅4.

-2+z(2⋅4)-z4=6

Factor z out of -z.

-2+z(2⋅4)+z⋅-14=6

Factor z out of z(2⋅4)+z⋅-1.

-2+z(2⋅4-1)4=6

-2+z(2⋅4-1)4=6

Multiply 2 by 4.

-2+z(8-1)4=6

Subtract 1 from 8.

-2+z⋅74=6

-2+z⋅74=6

Move 7 to the left of z.

-2+7z4=6

-2+7z4=6

-2+7z4=6

Add 2 to both sides of the equation.

7z4=6+2

Add 6 and 2.

7z4=8

7z4=8

Multiply both sides of the equation by 47.

47⋅7z4=47⋅8

Simplify 47⋅7z4.

Cancel the common factor of 4.

Cancel the common factor.

47⋅7z4=47⋅8

Rewrite the expression.

17⋅(7z)=47⋅8

17⋅(7z)=47⋅8

Cancel the common factor of 7.

Factor 7 out of 7z.

17⋅(7(z))=47⋅8

Cancel the common factor.

17⋅(7z)=47⋅8

Rewrite the expression.

z=47⋅8

z=47⋅8

z=47⋅8

Multiply 47⋅8.

Combine 47 and 8.

z=4⋅87

Multiply 4 by 8.

z=327

z=327

z=327

The result can be shown in multiple forms.

Exact Form:

z=327

Decimal Form:

z=4.571428‾

Mixed Number Form:

z=447

Solve for z 1/2z+2(3/4z-1)=1/4z+6