# Problem of the Week

## Updated at May 31, 2021 5:46 PM

For this week we've brought you this equation problem.

How would you solve the equation $$\frac{{(4(z+2))}^{2}}{6}=96$$?

Here are the steps:

$\frac{{(4(z+2))}^{2}}{6}=96$

 1 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$\frac{{4}^{2}{(z+2)}^{2}}{6}=96$2 Simplify  $${4}^{2}$$  to  $$16$$.$\frac{16{(z+2)}^{2}}{6}=96$3 Simplify  $$\frac{16{(z+2)}^{2}}{6}$$  to  $$\frac{8{(z+2)}^{2}}{3}$$.$\frac{8{(z+2)}^{2}}{3}=96$4 Multiply both sides by $$3$$.$8{(z+2)}^{2}=96\times 3$5 Simplify  $$96\times 3$$  to  $$288$$.$8{(z+2)}^{2}=288$6 Divide both sides by $$8$$.${(z+2)}^{2}=\frac{288}{8}$7 Simplify  $$\frac{288}{8}$$  to  $$36$$.${(z+2)}^{2}=36$8 Take the square root of both sides.$z+2=\pm \sqrt{36}$9 Since $$6\times 6=36$$, the square root of $$36$$ is $$6$$.$z+2=\pm 6$10 Break down the problem into these 2 equations.$z+2=6$$z+2=-6$11 Solve the 1st equation: $$z+2=6$$.1 Subtract $$2$$ from both sides.$z=6-2$2 Simplify  $$6-2$$  to  $$4$$.$z=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=4$12 Solve the 2nd equation: $$z+2=-6$$.1 Subtract $$2$$ from both sides.$z=-6-2$2 Simplify  $$-6-2$$  to  $$-8$$.$z=-8$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=-8$13 Collect all solutions.$z=4,-8$Done z=4,-8