144=(2x-2)(5+x)

Rewrite the equation as (2x-2)(5+x)=144.

(2x-2)(5+x)=144

Expand (2x-2)(5+x) using the FOIL Method.

Apply the distributive property.

2x(5+x)-2(5+x)=144

Apply the distributive property.

2x⋅5+2x⋅x-2(5+x)=144

Apply the distributive property.

2x⋅5+2x⋅x-2⋅5-2x=144

2x⋅5+2x⋅x-2⋅5-2x=144

Simplify and combine like terms.

Simplify each term.

Multiply 5 by 2.

10x+2x⋅x-2⋅5-2x=144

Multiply x by x by adding the exponents.

Move x.

10x+2(x⋅x)-2⋅5-2x=144

Multiply x by x.

10x+2×2-2⋅5-2x=144

10x+2×2-2⋅5-2x=144

Multiply -2 by 5.

10x+2×2-10-2x=144

10x+2×2-10-2x=144

Subtract 2x from 10x.

8x+2×2-10=144

8x+2×2-10=144

8x+2×2-10=144

Move 144 to the left side of the equation by subtracting it from both sides.

8x+2×2-10-144=0

Subtract 144 from -10.

8x+2×2-154=0

8x+2×2-154=0

Factor 2 out of 8x+2×2-154.

Factor 2 out of 8x.

2(4x)+2×2-154

Factor 2 out of 2×2.

2(4x)+2(x2)-154

Factor 2 out of -154.

2(4x)+2×2+2⋅-77

Factor 2 out of 2(4x)+2×2.

2(4x+x2)+2⋅-77

Factor 2 out of 2(4x+x2)+2⋅-77.

2(4x+x2-77)

2(4x+x2-77)

Let u=x. Substitute u for all occurrences of x.

2(4u+u2-77)

Factor 4u+u2-77 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 -77 and whose sum is 4.

-7,11

Write the factored form using these integers.

2((u-7)(u+11))

2((u-7)(u+11))

Factor.

Replace all occurrences of u with x.

2((x-7)(x+11))

Remove unnecessary parentheses.

2(x-7)(x+11)

2(x-7)(x+11)

Replace the left side with the factored expression.

2(x-7)(x+11)=0

2(x-7)(x+11)=0

Divide each term in 2(x-7)(x+11)=0 by 2.

2(x-7)(x+11)2=02

Cancel the common factor.

2(x-7)(x+11)2=02

Divide (x-7)(x+11) by 1.

(x-7)(x+11)=02

(x-7)(x+11)=02

Divide 0 by 2.

(x-7)(x+11)=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-7=0

x+11=0

Set the first factor equal to 0.

x-7=0

Add 7 to both sides of the equation.

x=7

x=7

Set the next factor equal to 0.

x+11=0

Subtract 11 from both sides of the equation.

x=-11

x=-11

The final solution is all the values that make 2(x-7)(x+11)2=02 true.

x=7,-11

Solve using the Square Root Property 144=(2x-2)(5+x)