4×2+7x-57=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=4⋅-57=-228 and whose sum is b=7.

Factor 7 out of 7x.

4×2+7(x)-57=0

Rewrite 7 as -12 plus 19

4×2+(-12+19)x-57=0

Apply the distributive property.

4×2-12x+19x-57=0

4×2-12x+19x-57=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(4×2-12x)+19x-57=0

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

4x(x-3)+19(x-3)=0

4x(x-3)+19(x-3)=0

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

(x-3)(4x+19)=0

(x-3)(4x+19)=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-3=0

4x+19=0

Set the first factor equal to 0.

x-3=0

Add 3 to both sides of the equation.

x=3

x=3

Set the next factor equal to 0.

4x+19=0

Subtract 19 from both sides of the equation.

4x=-19

Divide each term by 4 and simplify.

Divide each term in 4x=-19 by 4.

4×4=-194

Cancel the common factor of 4.

Cancel the common factor.

4×4=-194

Divide x by 1.

x=-194

x=-194

Move the negative in front of the fraction.

x=-194

x=-194

x=-194

The final solution is all the values that make (x-3)(4x+19)=0 true.

x=3,-194

Solve using the Square Root Property 4x^2+7x-57=0