36=12⋅(B(B+1))

Rewrite the equation as 12⋅(B(B+1))=36.

12⋅(B(B+1))=36

Multiply both sides of the equation by 2.

2⋅12⋅(B(B+1))=2⋅36

Simplify 2⋅12⋅(B(B+1)).

Cancel the common factor of 2.

Cancel the common factor.

2⋅12⋅(B(B+1))=2⋅36

Rewrite the expression.

1⋅(B(B+1))=2⋅36

1⋅(B(B+1))=2⋅36

Multiply B(B+1) by 1.

B(B+1)=2⋅36

Apply the distributive property.

B⋅B+B⋅1=2⋅36

Simplify the expression.

Multiply B by B.

B2+B⋅1=2⋅36

Multiply B by 1.

B2+B=2⋅36

B2+B=2⋅36

B2+B=2⋅36

Multiply 2 by 36.

B2+B=72

B2+B=72

Move 72 to the left side of the equation by subtracting it from both sides.

B2+B-72=0

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 -72 and whose sum is 1.

-8,9

Write the factored form using these integers.

(B-8)(B+9)=0

(B-8)(B+9)=0

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

B-8=0

B+9=0

Set the first factor equal to 0.

B-8=0

Add 8 to both sides of the equation.

B=8

B=8

Set the next factor equal to 0.

B+9=0

Subtract 9 from both sides of the equation.

B=-9

B=-9

The final solution is all the values that make (B-8)(B+9)=0 true.

B=8,-9

Solve for B 36=1/2*(B(B+1))