Solve for z 8(z+6)=4(2z+12)

$8 (z + 6) = 4 (2 z + 12)$

Simplify $8 (z + 6)$ .

Start simplifying.

$0 + 0 + 8 (z + 6) = 4 (2 z + 12)$

Simplify by adding zeros.

$8 (z + 6) = 4 (2 z + 12)$

Apply the distributive property.

$8 z + 8 \cdot 6 = 4 (2 z + 12)$

Multiply $8$ by $6$ .

$8 z + 48 = 4 (2 z + 12)$

Simplify $4 (2 z + 12)$ .

Apply the distributive property.

$8 z + 48 = 4 (2 z) + 4 \cdot 12$

Multiply.

Multiply $2$ by $4$ .

$8 z + 48 = 8 z + 4 \cdot 12$

Multiply $4$ by $12$ .

$8 z + 48 = 8 z + 48$

Move all terms containing $z$ to the left side of the equation.

Subtract $8 z$ from both sides of the equation.

$8 z + 48 - 8 z = 48$

Combine the opposite terms in $8 z + 48 - 8 z$ .

Subtract $8 z$ from $8 z$ .

$0 + 48 = 48$

Add $0$ and $48$ .

$48 = 48$

Since $48 = 48$ , the equation will always be true for any value of $z$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$