mgh=12⋅(mv2)

Rewrite the equation as 12⋅(mv2)=mgh.

12⋅(mv2)=mgh

Multiply both sides of the equation by 2.

2⋅12⋅(mv2)=2⋅(mgh)

Simplify 2⋅12⋅(mv2).

Cancel the common factor of 2.

Cancel the common factor.

2⋅12⋅(mv2)=2⋅(mgh)

Rewrite the expression.

1⋅(mv2)=2⋅(mgh)

1⋅(mv2)=2⋅(mgh)

Multiply mv2 by 1.

mv2=2⋅(mgh)

mv2=2⋅(mgh)

Remove parentheses.

mv2=2mgh

mv2=2mgh

Divide each term in mv2=2mgh by m.

mv2m=2mghm

Cancel the common factor of m.

Cancel the common factor.

mv2m=2mghm

Divide v2 by 1.

v2=2mghm

v2=2mghm

Cancel the common factor of m.

Cancel the common factor.

v2=2mghm

Divide 2gh by 1.

v2=2gh

v2=2gh

v2=2gh

Take the square root of both sides of the equation to eliminate the exponent on the left side.

v=±2gh

First, use the positive value of the ± to find the first solution.

v=2gh

Next, use the negative value of the ± to find the second solution.

v=-2gh

The complete solution is the result of both the positive and negative portions of the solution.

v=2gh

v=-2gh

v=2gh

v=-2gh

Solve for v mgh=1/2*(mv^2)