c(13c+5)=8

Simplify by multiplying through.

Apply the distributive property.

c(13c)+c⋅5=8

Reorder.

Rewrite using the commutative property of multiplication.

13c⋅c+c⋅5=8

Move 5 to the left of c.

13c⋅c+5⋅c=8

13c⋅c+5⋅c=8

13c⋅c+5⋅c=8

Multiply c by c by adding the exponents.

Move c.

13(c⋅c)+5⋅c=8

Multiply c by c.

13c2+5⋅c=8

13c2+5c=8

13c2+5c=8

Move 8 to the left side of the equation by subtracting it from both sides.

13c2+5c-8=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=13⋅-8=-104 and whose sum is b=5.

Factor 5 out of 5c.

13c2+5(c)-8=0

Rewrite 5 as -8 plus 13

13c2+(-8+13)c-8=0

Apply the distributive property.

13c2-8c+13c-8=0

13c2-8c+13c-8=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(13c2-8c)+13c-8=0

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

c(13c-8)+1(13c-8)=0

c(13c-8)+1(13c-8)=0

Factor the polynomial by factoring out the greatest common factor, 13c-8.

(13c-8)(c+1)=0

(13c-8)(c+1)=0

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

13c-8=0

c+1=0

Set the first factor equal to 0.

13c-8=0

Add 8 to both sides of the equation.

13c=8

Divide each term by 13 and simplify.

Divide each term in 13c=8 by 13.

13c13=813

Cancel the common factor of 13.

Cancel the common factor.

13c13=813

Divide c by 1.

c=813

c=813

c=813

c=813

Set the next factor equal to 0.

c+1=0

Subtract 1 from both sides of the equation.

c=-1

c=-1

The final solution is all the values that make (13c-8)(c+1)=0 true.

c=813,-1

The result can be shown in multiple forms.

Exact Form:

c=813,-1

Decimal Form:

c=0.615384‾,-1

Solve for c c(13c+5)=8