# Solve for d 75d^3+50d^2-3d-2=0 75d3+50d2-3d-2=0
Factor the left side of the equation.
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 and solve.
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 and solve.
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 and solve.
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

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