a(a-7)=30

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

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.

a-10=0

Add 10 to both sides of the equation.

a=10

a=10

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