3×2+7x-18=6-7x

Add 7x to both sides of the equation.

3×2+7x-18+7x=6

Add 7x and 7x.

3×2+14x-18=6

3×2+14x-18=6

Move 6 to the left side of the equation by subtracting it from both sides.

3×2+14x-18-6=0

Subtract 6 from -18.

3×2+14x-24=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=3⋅-24=-72 and whose sum is b=14.

Factor 14 out of 14x.

3×2+14(x)-24=0

Rewrite 14 as -4 plus 18

3×2+(-4+18)x-24=0

Apply the distributive property.

3×2-4x+18x-24=0

3×2-4x+18x-24=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2-4x)+18x-24=0

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

x(3x-4)+6(3x-4)=0

x(3x-4)+6(3x-4)=0

Factor the polynomial by factoring out the greatest common factor, 3x-4.

(3x-4)(x+6)=0

(3x-4)(x+6)=0

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

3x-4=0

x+6=0

Set the first 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

Set the next factor equal to 0.

x+6=0

Subtract 6 from both sides of the equation.

x=-6

x=-6

The final solution is all the values that make (3x-4)(x+6)=0 true.

x=43,-6

Solve Using the Square Root Property 3x^2+7x-18=6-7x