18×2-15x-12=0

Factor 3 out of 18×2-15x-12.

Factor 3 out of 18×2.

3(6×2)-15x-12=0

Factor 3 out of -15x.

3(6×2)+3(-5x)-12=0

Factor 3 out of -12.

3(6×2)+3(-5x)+3(-4)=0

Factor 3 out of 3(6×2)+3(-5x).

3(6×2-5x)+3(-4)=0

Factor 3 out of 3(6×2-5x)+3(-4).

3(6×2-5x-4)=0

3(6×2-5x-4)=0

Factor.

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅-4=-24 and whose sum is b=-5.

Factor -5 out of -5x.

3(6×2-5x-4)=0

Rewrite -5 as 3 plus -8

3(6×2+(3-8)x-4)=0

Apply the distributive property.

3(6×2+3x-8x-4)=0

3(6×2+3x-8x-4)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

3((6×2+3x)-8x-4)=0

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

3(3x(2x+1)-4(2x+1))=0

3(3x(2x+1)-4(2x+1))=0

Factor the polynomial by factoring out the greatest common factor, 2x+1.

3((2x+1)(3x-4))=0

3((2x+1)(3x-4))=0

Remove unnecessary parentheses.

3(2x+1)(3x-4)=0

3(2x+1)(3x-4)=0

3(2x+1)(3x-4)=0

Divide each term in 3(2x+1)(3x-4)=0 by 3.

3(2x+1)(3x-4)3=03

Simplify 3(2x+1)(3x-4)3.

Cancel the common factor of 3.

Cancel the common factor.

3(2x+1)(3x-4)3=03

Divide (2x+1)(3x-4) by 1.

(2x+1)(3x-4)=03

(2x+1)(3x-4)=03

Expand (2x+1)(3x-4) using the FOIL Method.

Apply the distributive property.

2x(3x-4)+1(3x-4)=03

Apply the distributive property.

2x(3x)+2x⋅-4+1(3x-4)=03

Apply the distributive property.

2x(3x)+2x⋅-4+1(3x)+1⋅-4=03

2x(3x)+2x⋅-4+1(3x)+1⋅-4=03

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

2⋅3×2+2x⋅-4+1(3x)+1⋅-4=03

Multiply 2 by 3.

6×2+2x⋅-4+1(3x)+1⋅-4=03

Multiply -4 by 2.

6×2-8x+1(3x)+1⋅-4=03

Multiply 3x by 1.

6×2-8x+3x+1⋅-4=03

Multiply -4 by 1.

6×2-8x+3x-4=03

6×2-8x+3x-4=03

Add -8x and 3x.

6×2-5x-4=03

6×2-5x-4=03

6×2-5x-4=03

Divide 0 by 3.

6×2-5x-4=0

6×2-5x-4=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=6⋅-4=-24 and whose sum is b=-5.

Factor -5 out of -5x.

6×2-5x-4=0

Rewrite -5 as 3 plus -8

6×2+(3-8)x-4=0

Apply the distributive property.

6×2+3x-8x-4=0

6×2+3x-8x-4=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(6×2+3x)-8x-4=0

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

3x(2x+1)-4(2x+1)=0

3x(2x+1)-4(2x+1)=0

Factor the polynomial by factoring out the greatest common factor, 2x+1.

(2x+1)(3x-4)=0

(2x+1)(3x-4)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

2x+1=0

3x-4=0

Set the first factor equal to 0.

2x+1=0

Subtract 1 from both sides of the equation.

2x=-1

Divide each term by 2 and simplify.

Divide each term in 2x=-1 by 2.

2×2=-12

Cancel the common factor of 2.

Cancel the common factor.

2×2=-12

Divide x by 1.

x=-12

x=-12

Move the negative in front of the fraction.

x=-12

x=-12

x=-12

Set the next factor equal to 0.

3x-4=0

Add 4 to both sides of the equation.

3x=4

Divide each term by 3 and simplify.

Divide each term in 3x=4 by 3.

3×3=43

Cancel the common factor of 3.

Cancel the common factor.

3×3=43

Divide x by 1.

x=43

x=43

x=43

x=43

The final solution is all the values that make (2x+1)(3x-4)=0 true.

x=-12,43

Solve Using the Square Root Property 18x^2-15x-12=0