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

c(13c+5)=8
Simplify c(13c+5).
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
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=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 and solve.
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 and solve.
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

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