8x-1+6×2=7

Move 7 to the left side of the equation by subtracting it from both sides.

8x-1+6×2-7=0

Subtract 7 from -1.

8x+6×2-8=0

Factor 2 out of 8x+6×2-8.

Factor 2 out of 8x.

2(4x)+6×2-8=0

Factor 2 out of 6×2.

2(4x)+2(3×2)-8=0

Factor 2 out of -8.

2(4x)+2(3×2)+2(-4)=0

Factor 2 out of 2(4x)+2(3×2).

2(4x+3×2)+2(-4)=0

Factor 2 out of 2(4x+3×2)+2(-4).

2(4x+3×2-4)=0

2(4x+3×2-4)=0

Let u=x. Substitute u for all occurrences of x.

2(4u+3u2-4)=0

Factor by grouping.

Reorder terms.

2(3u2+4u-4)=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⋅-4=-12 and whose sum is b=4.

Factor 4 out of 4u.

2(3u2+4(u)-4)=0

Rewrite 4 as -2 plus 6

2(3u2+(-2+6)u-4)=0

Apply the distributive property.

2(3u2-2u+6u-4)=0

2(3u2-2u+6u-4)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2((3u2-2u)+6u-4)=0

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

2(u(3u-2)+2(3u-2))=0

2(u(3u-2)+2(3u-2))=0

Factor the polynomial by factoring out the greatest common factor, 3u-2.

2((3u-2)(u+2))=0

2((3u-2)(u+2))=0

Factor.

Replace all occurrences of u with x.

2((3x-2)(x+2))=0

Remove unnecessary parentheses.

2(3x-2)(x+2)=0

2(3x-2)(x+2)=0

2(3x-2)(x+2)=0

Divide each term in 2(3x-2)(x+2)=0 by 2.

2(3x-2)(x+2)2=02

Simplify 2(3x-2)(x+2)2.

Cancel the common factor of 2.

Cancel the common factor.

2(3x-2)(x+2)2=02

Divide (3x-2)(x+2) by 1.

(3x-2)(x+2)=02

(3x-2)(x+2)=02

Expand (3x-2)(x+2) using the FOIL Method.

Apply the distributive property.

3x(x+2)-2(x+2)=02

Apply the distributive property.

3x⋅x+3x⋅2-2(x+2)=02

Apply the distributive property.

3x⋅x+3x⋅2-2x-2⋅2=02

3x⋅x+3x⋅2-2x-2⋅2=02

Simplify and combine like terms.

Simplify each term.

Multiply x by x by adding the exponents.

Move x.

3(x⋅x)+3x⋅2-2x-2⋅2=02

Multiply x by x.

3×2+3x⋅2-2x-2⋅2=02

3×2+3x⋅2-2x-2⋅2=02

Multiply 2 by 3.

3×2+6x-2x-2⋅2=02

Multiply -2 by 2.

3×2+6x-2x-4=02

3×2+6x-2x-4=02

Subtract 2x from 6x.

3×2+4x-4=02

3×2+4x-4=02

3×2+4x-4=02

Divide 0 by 2.

3×2+4x-4=0

3×2+4x-4=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⋅-4=-12 and whose sum is b=4.

Factor 4 out of 4x.

3×2+4(x)-4=0

Rewrite 4 as -2 plus 6

3×2+(-2+6)x-4=0

Apply the distributive property.

3×2-2x+6x-4=0

3×2-2x+6x-4=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2-2x)+6x-4=0

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

x(3x-2)+2(3x-2)=0

x(3x-2)+2(3x-2)=0

Factor the polynomial by factoring out the greatest common factor, 3x-2.

(3x-2)(x+2)=0

(3x-2)(x+2)=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-2=0

x+2=0

Set the first factor equal to 0.

3x-2=0

Add 2 to both sides of the equation.

3x=2

Divide each term by 3 and simplify.

Divide each term in 3x=2 by 3.

3×3=23

Cancel the common factor of 3.

Cancel the common factor.

3×3=23

Divide x by 1.

x=23

x=23

x=23

x=23

Set the next factor equal to 0.

x+2=0

Subtract 2 from both sides of the equation.

x=-2

x=-2

The final solution is all the values that make (3x-2)(x+2)=0 true.

x=23,-2

Solve using the Square Root Property 8x-1+6x^2=7