(6n+1)2+5(6n+1)-6=0

Let u=6n+1. Substitute u for all occurrences of 6n+1.

u2+5u-6

Factor u2+5u-6 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is 5.

-1,6

Write the factored form using these integers.

(u-1)(u+6)

(u-1)(u+6)

Replace all occurrences of u with 6n+1.

(6n+1-1)(6n+1+6)

Simplify.

Combine the opposite terms in 6n+1-1.

Subtract 1 from 1.

(6n+0)(6n+1+6)

Add 6n and 0.

6n(6n+1+6)

6n(6n+1+6)

Add 1 and 6.

6n(6n+7)

6n(6n+7)

Replace the left side with the factored expression.

6n(6n+7)=0

6n(6n+7)=0

Divide each term in 6n(6n+7)=0 by 6.

6n(6n+7)6=06

Cancel the common factor.

6n(6n+7)6=06

Divide n(6n+7) by 1.

n(6n+7)=06

n(6n+7)=06

Divide 0 by 6.

n(6n+7)=0

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

n=0

6n+7=0

Set the first factor equal to 0.

n=0

Set the next factor equal to 0.

6n+7=0

Subtract 7 from both sides of the equation.

6n=-7

Divide each term by 6 and simplify.

Divide each term in 6n=-7 by 6.

6n6=-76

Cancel the common factor of 6.

Cancel the common factor.

6n6=-76

Divide n by 1.

n=-76

n=-76

Move the negative in front of the fraction.

n=-76

n=-76

n=-76

The final solution is all the values that make 6n(6n+7)6=06 true.

n=0,-76

The result can be shown in multiple forms.

Exact Form:

n=0,-76

Decimal Form:

n=0,-1.16‾

Mixed Number Form:

n=0,-116

Solve for n (6n+1)^2+5(6n+1)-6=0