(x-2)(x+4)=7

Expand (x-2)(x+4) using the FOIL Method.

Apply the distributive property.

x(x+4)-2(x+4)=7

Apply the distributive property.

x⋅x+x⋅4-2(x+4)=7

Apply the distributive property.

x⋅x+x⋅4-2x-2⋅4=7

x⋅x+x⋅4-2x-2⋅4=7

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2+x⋅4-2x-2⋅4=7

Move 4 to the left of x.

x2+4⋅x-2x-2⋅4=7

Multiply -2 by 4.

x2+4x-2x-8=7

x2+4x-2x-8=7

Subtract 2x from 4x.

x2+2x-8=7

x2+2x-8=7

x2+2x-8=7

Move 7 to the left side of the equation by subtracting it from both sides.

x2+2x-8-7=0

Subtract 7 from -8.

x2+2x-15=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 -15 and whose sum is 2.

-3,5

Write the factored form using these integers.

(x-3)(x+5)=0

(x-3)(x+5)=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-3=0

x+5=0

Set the first factor equal to 0.

x-3=0

Add 3 to both sides of the equation.

x=3

x=3

Set the next factor equal to 0.

x+5=0

Subtract 5 from both sides of the equation.

x=-5

x=-5

The final solution is all the values that make (x-3)(x+5)=0 true.

x=3,-5

Solve for x (x-2)(x+4)=7