# Solve for a a(a-7)=18 a(a-7)=18
Simplify a(a-7).
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
Factor a2-7a-18 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 -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 and solve.
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 and solve.
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

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