7×2+4x-12=44-37x

Add 37x to both sides of the equation.

7×2+4x-12+37x=44

Add 4x and 37x.

7×2+41x-12=44

7×2+41x-12=44

Move 44 to the left side of the equation by subtracting it from both sides.

7×2+41x-12-44=0

Subtract 44 from -12.

7×2+41x-56=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=7⋅-56=-392 and whose sum is b=41.

Factor 41 out of 41x.

7×2+41(x)-56=0

Rewrite 41 as -8 plus 49

7×2+(-8+49)x-56=0

Apply the distributive property.

7×2-8x+49x-56=0

7×2-8x+49x-56=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(7×2-8x)+49x-56=0

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

x(7x-8)+7(7x-8)=0

x(7x-8)+7(7x-8)=0

Factor the polynomial by factoring out the greatest common factor, 7x-8.

(7x-8)(x+7)=0

(7x-8)(x+7)=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-8=0

x+7=0

Set the first factor equal to 0.

7x-8=0

Add 8 to both sides of the equation.

7x=8

Divide each term by 7 and simplify.

Divide each term in 7x=8 by 7.

7×7=87

Cancel the common factor of 7.

Cancel the common factor.

7×7=87

Divide x by 1.

x=87

x=87

x=87

x=87

Set the next factor equal to 0.

x+7=0

Subtract 7 from both sides of the equation.

x=-7

x=-7

The final solution is all the values that make (7x-8)(x+7)=0 true.

x=87,-7

Solve Using the Square Root Property 7x^2+4x-12=44-37x