(4z+3)(4-z)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

4z+3=0

4-z=0

Set the first factor equal to 0.

4z+3=0

Subtract 3 from both sides of the equation.

4z=-3

Divide each term by 4 and simplify.

Divide each term in 4z=-3 by 4.

4z4=-34

Cancel the common factor of 4.

Cancel the common factor.

4z4=-34

Divide z by 1.

z=-34

z=-34

Move the negative in front of the fraction.

z=-34

z=-34

z=-34

Set the next factor equal to 0.

4-z=0

Subtract 4 from both sides of the equation.

-z=-4

Multiply each term in -z=-4 by -1

Multiply each term in -z=-4 by -1.

(-z)⋅-1=(-4)⋅-1

Multiply (-z)⋅-1.

Multiply -1 by -1.

1z=(-4)⋅-1

Multiply z by 1.

z=(-4)⋅-1

z=(-4)⋅-1

Multiply -4 by -1.

z=4

z=4

z=4

The final solution is all the values that make (4z+3)(4-z)=0 true.

z=-34,4

The result can be shown in multiple forms.

Exact Form:

z=-34,4

Decimal Form:

z=-0.75,4

Solve for z (4z+3)(4-z)=0