Algebra Examples

Find the Roots (Zeros) 3x^3+x^2-15x-5
Step 1
Set equal to .
Step 2
Solve for .
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Step 2.1
Factor the left side of the equation.
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Step 2.1.1
Factor out the greatest common factor from each group.
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Step 2.1.1.1
Group the first two terms and the last two terms.
Step 2.1.1.2
Factor out the greatest common factor (GCF) from each group.
Step 2.1.2
Factor the polynomial by factoring out the greatest common factor, .
Step 2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.3
Set equal to and solve for .
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Step 2.3.1
Set equal to .
Step 2.3.2
Solve for .
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Step 2.3.2.1
Subtract from both sides of the equation.
Step 2.3.2.2
Divide each term in by and simplify.
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Step 2.3.2.2.1
Divide each term in by .
Step 2.3.2.2.2
Simplify the left side.
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Step 2.3.2.2.2.1
Cancel the common factor of .
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Step 2.3.2.2.2.1.1
Cancel the common factor.
Step 2.3.2.2.2.1.2
Divide by .
Step 2.3.2.2.3
Simplify the right side.
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Step 2.3.2.2.3.1
Move the negative in front of the fraction.
Step 2.4
Set equal to and solve for .
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Step 2.4.1
Set equal to .
Step 2.4.2
Solve for .
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Step 2.4.2.1
Add to both sides of the equation.
Step 2.4.2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.4.2.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.4.2.3.1
First, use the positive value of the to find the first solution.
Step 2.4.2.3.2
Next, use the negative value of the to find the second solution.
Step 2.4.2.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.5
The final solution is all the values that make true.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Step 4