# Solve for n (6n+1)^2+5(6n+1)-6=0 (6n+1)2+5(6n+1)-6=0
Factor the left side of the equation.
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 of 6.
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 and solve.
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

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