2x(x+1)=12

Divide each term in 2x(x+1)=12 by 2.

2x(x+1)2=122

Simplify 2x(x+1)2.

Cancel the common factor of 2.

Cancel the common factor.

2x(x+1)2=122

Divide x(x+1) by 1.

x(x+1)=122

x(x+1)=122

Apply the distributive property.

x⋅x+x⋅1=122

Simplify the expression.

Multiply x by x.

x2+x⋅1=122

Multiply x by 1.

x2+x=122

x2+x=122

x2+x=122

Divide 12 by 2.

x2+x=6

x2+x=6

Move 6 to the left side of the equation by subtracting it from both sides.

x2+x-6=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 -6 and whose sum is 1.

-2,3

Write the factored form using these integers.

(x-2)(x+3)=0

(x-2)(x+3)=0

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

x-2=0

x+3=0

Set the first factor equal to 0.

x-2=0

Add 2 to both sides of the equation.

x=2

x=2

Set the next factor equal to 0.

x+3=0

Subtract 3 from both sides of the equation.

x=-3

x=-3

The final solution is all the values that make (x-2)(x+3)=0 true.

x=2,-3

Solve Using the Square Root Property 2x(x+1)=12