75d3+50d2-3d-2=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(75d3+50d2)-3d-2=0

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

25d2(3d+2)-(3d+2)=0

25d2(3d+2)-(3d+2)=0

Factor the polynomial by factoring out the greatest common factor, 3d+2.

(3d+2)(25d2-1)=0

Rewrite 25d2 as (5d)2.

(3d+2)((5d)2-1)=0

Rewrite 1 as 12.

(3d+2)((5d)2-12)=0

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=5d and b=1.

(3d+2)((5d+1)(5d-1))=0

Remove unnecessary parentheses.

(3d+2)(5d+1)(5d-1)=0

(3d+2)(5d+1)(5d-1)=0

(3d+2)(5d+1)(5d-1)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

3d+2=0

5d+1=0

5d-1=0

Set the first factor equal to 0.

3d+2=0

Subtract 2 from both sides of the equation.

3d=-2

Divide each term by 3 and simplify.

Divide each term in 3d=-2 by 3.

3d3=-23

Cancel the common factor of 3.

Cancel the common factor.

3d3=-23

Divide d by 1.

d=-23

d=-23

Move the negative in front of the fraction.

d=-23

d=-23

d=-23

Set the next factor equal to 0.

5d+1=0

Subtract 1 from both sides of the equation.

5d=-1

Divide each term by 5 and simplify.

Divide each term in 5d=-1 by 5.

5d5=-15

Cancel the common factor of 5.

Cancel the common factor.

5d5=-15

Divide d by 1.

d=-15

d=-15

Move the negative in front of the fraction.

d=-15

d=-15

d=-15

Set the next factor equal to 0.

5d-1=0

Add 1 to both sides of the equation.

5d=1

Divide each term by 5 and simplify.

Divide each term in 5d=1 by 5.

5d5=15

Cancel the common factor of 5.

Cancel the common factor.

5d5=15

Divide d by 1.

d=15

d=15

d=15

d=15

The final solution is all the values that make (3d+2)(5d+1)(5d-1)=0 true.

d=-23,-15,15

The result can be shown in multiple forms.

Exact Form:

d=-23,-15,15

Decimal Form:

d=-0.6‾,-0.2,0.2

Solve for d 75d^3+50d^2-3d-2=0