a(a-7)=18

Apply the distributive property.

a⋅a+a⋅-7=18

Simplify the expression.

Multiply a by a.

a2+a⋅-7=18

Move -7 to the left of a.

a2-7a=18

a2-7a=18

a2-7a=18

Move 18 to the left side of the equation by subtracting it from both sides.

a2-7a-18=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 -18 and whose sum is -7.

-9,2

Write the factored form using these integers.

(a-9)(a+2)=0

(a-9)(a+2)=0

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

a-9=0

a+2=0

Set the first factor equal to 0.

a-9=0

Add 9 to both sides of the equation.

a=9

a=9

Set the next factor equal to 0.

a+2=0

Subtract 2 from both sides of the equation.

a=-2

a=-2

The final solution is all the values that make (a-9)(a+2)=0 true.

a=9,-2

Solve for a a(a-7)=18