29n2-160n+256=5n2

Subtract 5n2 from both sides of the equation.

29n2-160n+256-5n2=0

Subtract 5n2 from 29n2.

24n2-160n+256=0

24n2-160n+256=0

Factor 8 out of 24n2-160n+256.

Factor 8 out of 24n2.

8(3n2)-160n+256=0

Factor 8 out of -160n.

8(3n2)+8(-20n)+256=0

Factor 8 out of 256.

8(3n2)+8(-20n)+8(32)=0

Factor 8 out of 8(3n2)+8(-20n).

8(3n2-20n)+8(32)=0

Factor 8 out of 8(3n2-20n)+8(32).

8(3n2-20n+32)=0

8(3n2-20n+32)=0

Factor.

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅32=96 and whose sum is b=-20.

Factor -20 out of -20n.

8(3n2-20n+32)=0

Rewrite -20 as -8 plus -12

8(3n2+(-8-12)n+32)=0

Apply the distributive property.

8(3n2-8n-12n+32)=0

8(3n2-8n-12n+32)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

8((3n2-8n)-12n+32)=0

Factor out the greatest common factor (GCF) from each group.

8(n(3n-8)-4(3n-8))=0

8(n(3n-8)-4(3n-8))=0

Factor the polynomial by factoring out the greatest common factor, 3n-8.

8((3n-8)(n-4))=0

8((3n-8)(n-4))=0

Remove unnecessary parentheses.

8(3n-8)(n-4)=0

8(3n-8)(n-4)=0

8(3n-8)(n-4)=0

Divide each term in 8(3n-8)(n-4)=0 by 8.

8(3n-8)(n-4)8=08

Simplify 8(3n-8)(n-4)8.

Cancel the common factor of 8.

Cancel the common factor.

8(3n-8)(n-4)8=08

Divide (3n-8)(n-4) by 1.

(3n-8)(n-4)=08

(3n-8)(n-4)=08

Expand (3n-8)(n-4) using the FOIL Method.

Apply the distributive property.

3n(n-4)-8(n-4)=08

Apply the distributive property.

3n⋅n+3n⋅-4-8(n-4)=08

Apply the distributive property.

3n⋅n+3n⋅-4-8n-8⋅-4=08

3n⋅n+3n⋅-4-8n-8⋅-4=08

Simplify and combine like terms.

Simplify each term.

Multiply n by n by adding the exponents.

Move n.

3(n⋅n)+3n⋅-4-8n-8⋅-4=08

Multiply n by n.

3n2+3n⋅-4-8n-8⋅-4=08

3n2+3n⋅-4-8n-8⋅-4=08

Multiply -4 by 3.

3n2-12n-8n-8⋅-4=08

Multiply -8 by -4.

3n2-12n-8n+32=08

3n2-12n-8n+32=08

Subtract 8n from -12n.

3n2-20n+32=08

3n2-20n+32=08

3n2-20n+32=08

Divide 0 by 8.

3n2-20n+32=0

3n2-20n+32=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅32=96 and whose sum is b=-20.

Factor -20 out of -20n.

3n2-20n+32=0

Rewrite -20 as -8 plus -12

3n2+(-8-12)n+32=0

Apply the distributive property.

3n2-8n-12n+32=0

3n2-8n-12n+32=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3n2-8n)-12n+32=0

Factor out the greatest common factor (GCF) from each group.

n(3n-8)-4(3n-8)=0

n(3n-8)-4(3n-8)=0

Factor the polynomial by factoring out the greatest common factor, 3n-8.

(3n-8)(n-4)=0

(3n-8)(n-4)=0

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

3n-8=0

n-4=0

Set the first factor equal to 0.

3n-8=0

Add 8 to both sides of the equation.

3n=8

Divide each term by 3 and simplify.

Divide each term in 3n=8 by 3.

3n3=83

Cancel the common factor of 3.

Cancel the common factor.

3n3=83

Divide n by 1.

n=83

n=83

n=83

n=83

Set the next factor equal to 0.

n-4=0

Add 4 to both sides of the equation.

n=4

n=4

The final solution is all the values that make (3n-8)(n-4)=0 true.

n=83,4

The result can be shown in multiple forms.

Exact Form:

n=83,4

Decimal Form:

n=2.6‾,4

Mixed Number Form:

n=223,4

Solve for n 29n^2-160n+256=5n^2