3×2-13x=-12

Move 12 to the left side of the equation by adding it to both sides.

3×2-13x+12=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⋅12=36 and whose sum is b=-13.

Factor -13 out of -13x.

3×2-13x+12=0

Rewrite -13 as -4 plus -9

3×2+(-4-9)x+12=0

Apply the distributive property.

3×2-4x-9x+12=0

3×2-4x-9x+12=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2-4x)-9x+12=0

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

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

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

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

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

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

Add 3 to both sides of the equation.

x=3

x=3

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

x=43,3

Solve Using the Square Root Property 3x^2-13x=-12