# Solve for a a(a-7)=30

a(a-7)=30
Simplify a(a-7).
Apply the distributive property.
a⋅a+a⋅-7=30
Simplify the expression.
Multiply a by a.
a2+a⋅-7=30
Move -7 to the left of a.
a2-7a=30
a2-7a=30
a2-7a=30
Move 30 to the left side of the equation by subtracting it from both sides.
a2-7a-30=0
Factor a2-7a-30 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 -30 and whose sum is -7.
-10,3
Write the factored form using these integers.
(a-10)(a+3)=0
(a-10)(a+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.
a-10=0
a+3=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
a-10=0
Add 10 to both sides of the equation.
a=10
a=10
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
a+3=0
Subtract 3 from both sides of the equation.
a=-3
a=-3
The final solution is all the values that make (a-10)(a+3)=0 true.
a=10,-3
Solve for a a(a-7)=30

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