21×2=-23x+20

Add 23x to both sides of the equation.

21×2+23x=20

Move 20 to the left side of the equation by subtracting it from both sides.

21×2+23x-20=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=21⋅-20=-420 and whose sum is b=23.

Factor 23 out of 23x.

21×2+23(x)-20=0

Rewrite 23 as -12 plus 35

21×2+(-12+35)x-20=0

Apply the distributive property.

21×2-12x+35x-20=0

21×2-12x+35x-20=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(21×2-12x)+35x-20=0

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

3x(7x-4)+5(7x-4)=0

3x(7x-4)+5(7x-4)=0

Factor the polynomial by factoring out the greatest common factor, 7x-4.

(7x-4)(3x+5)=0

(7x-4)(3x+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.

7x-4=0

3x+5=0

Set the first factor equal to 0.

7x-4=0

Add 4 to both sides of the equation.

7x=4

Divide each term by 7 and simplify.

Divide each term in 7x=4 by 7.

7×7=47

Cancel the common factor of 7.

Cancel the common factor.

7×7=47

Divide x by 1.

x=47

x=47

x=47

x=47

Set the next factor equal to 0.

3x+5=0

Subtract 5 from both sides of the equation.

3x=-5

Divide each term by 3 and simplify.

Divide each term in 3x=-5 by 3.

3×3=-53

Cancel the common factor of 3.

Cancel the common factor.

3×3=-53

Divide x by 1.

x=-53

x=-53

Move the negative in front of the fraction.

x=-53

x=-53

x=-53

The final solution is all the values that make (7x-4)(3x+5)=0 true.

x=47,-53

Solve Using the Square Root Property 21x^2=-23x+20