120=(2x+1)(x+1)

Rewrite the equation as (2x+1)(x+1)=120.

(2x+1)(x+1)=120

Expand (2x+1)(x+1) using the FOIL Method.

Apply the distributive property.

2x(x+1)+1(x+1)=120

Apply the distributive property.

2x⋅x+2x⋅1+1(x+1)=120

Apply the distributive property.

2x⋅x+2x⋅1+1x+1⋅1=120

2x⋅x+2x⋅1+1x+1⋅1=120

Simplify and combine like terms.

Simplify each term.

Multiply x by x by adding the exponents.

Move x.

2(x⋅x)+2x⋅1+1x+1⋅1=120

Multiply x by x.

2×2+2x⋅1+1x+1⋅1=120

2×2+2x⋅1+1x+1⋅1=120

Multiply 2 by 1.

2×2+2x+1x+1⋅1=120

Multiply x by 1.

2×2+2x+x+1⋅1=120

Multiply 1 by 1.

2×2+2x+x+1=120

2×2+2x+x+1=120

Add 2x and x.

2×2+3x+1=120

2×2+3x+1=120

2×2+3x+1=120

Move 120 to the left side of the equation by subtracting it from both sides.

2×2+3x+1-120=0

Subtract 120 from 1.

2×2+3x-119=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-119=-238 and whose sum is b=3.

Factor 3 out of 3x.

2×2+3(x)-119=0

Rewrite 3 as -14 plus 17

2×2+(-14+17)x-119=0

Apply the distributive property.

2×2-14x+17x-119=0

2×2-14x+17x-119=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2×2-14x)+17x-119=0

Factor out the greatest common factor (GCF) from each group.

2x(x-7)+17(x-7)=0

2x(x-7)+17(x-7)=0

Factor the polynomial by factoring out the greatest common factor, x-7.

(x-7)(2x+17)=0

(x-7)(2x+17)=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

2x+17=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.

2x+17=0

Subtract 17 from both sides of the equation.

2x=-17

Divide each term by 2 and simplify.

Divide each term in 2x=-17 by 2.

2×2=-172

Cancel the common factor of 2.

Cancel the common factor.

2×2=-172

Divide x by 1.

x=-172

x=-172

Move the negative in front of the fraction.

x=-172

x=-172

x=-172

The final solution is all the values that make (x-7)(2x+17)=0 true.

x=7,-172

Solve Using the Square Root Property 120=(2x+1)(x+1)