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

12⋅(mv2)=mgh
Multiply 12(mv2).
Combine m and 12.
m2v2=mgh
Combine m2 and v2.
mv22=mgh
mv22=mgh
Subtract mgh from both sides of the equation.
mv22-mgh=0
Factor m out of mv22-mgh.
Factor m out of mv22.
m(v22)-mgh=0
Factor m out of -mgh.
m(v22)+m(-1gh)=0
Factor m out of mv22+m(-1gh).
m(v22-1gh)=0
m(v22-1gh)=0
Rewrite -1g as -g.
m(v22-gh)=0
Divide each term by v22-gh and simplify.
Divide each term in m(v22-gh)=0 by v22-gh.
m(v22-gh)v22-gh=0v22-gh
Cancel the common factor of v22-gh.
Cancel the common factor.
m(v22-gh)v22-gh=0v22-gh
Divide m by 1.
m=0v22-gh
m=0v22-gh
Simplify 0v22-gh.
Simplify the denominator.
To write -gh as a fraction with a common denominator, multiply by 22.
m=0v22-gh⋅22
Combine -gh and 22.
m=0v22+-gh⋅22
Combine the numerators over the common denominator.
m=0v2-gh⋅22
Multiply 2 by -1.
m=0v2-2gh2
m=0v2-2gh2
Multiply the numerator by the reciprocal of the denominator.
m=02v2-2gh
Multiply 0 by 2v2-2gh.
m=0
m=0
m=0
Solve for m 1/2*(mv^2)=mgh

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