x(x-1)=12

Simplify by multiplying through.

Apply the distributive property.

x⋅x+x⋅-1=12

Simplify the expression.

Multiply x by x.

x2+x⋅-1=12

Move -1 to the left of x.

x2-1⋅x=12

x2-1⋅x=12

x2-1⋅x=12

Rewrite -1x as -x.

x2-x=12

x2-x=12

Move 12 to the left side of the equation by subtracting it from both sides.

x2-x-12=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 -12 and whose sum is -1.

-4,3

Write the factored form using these integers.

(x-4)(x+3)=0

(x-4)(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-4=0

x+3=0

Set the first factor equal to 0.

x-4=0

Add 4 to both sides of the equation.

x=4

x=4

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-4)(x+3)=0 true.

x=4,-3

Solve using the Square Root Property x(x-1)=12