# Solve for x (x-2)(x+4)=7 (x-2)(x+4)=7
Simplify (x-2)(x+4).
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
Factor x2+2x-15 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 -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 and solve.
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 and solve.
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     