Basic Math Examples

Solve for n (4n+1)^2+3(4n+1)-4=0
Step 1
Factor the left side of the equation.
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Step 1.1
Let . Substitute for all occurrences of .
Step 1.2
Factor using the AC method.
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Step 1.2.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 1.2.2
Write the factored form using these integers.
Step 1.3
Replace all occurrences of with .
Step 2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3
Set equal to and solve for .
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Step 3.1
Set equal to .
Step 3.2
Solve for .
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Step 3.2.1
Combine the opposite terms in .
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Step 3.2.1.1
Subtract from .
Step 3.2.1.2
Add and .
Step 3.2.2
Divide each term in by and simplify.
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Step 3.2.2.1
Divide each term in by .
Step 3.2.2.2
Simplify the left side.
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Step 3.2.2.2.1
Cancel the common factor of .
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Step 3.2.2.2.1.1
Cancel the common factor.
Step 3.2.2.2.1.2
Divide by .
Step 3.2.2.3
Simplify the right side.
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Step 3.2.2.3.1
Divide by .
Step 4
Set equal to and solve for .
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Step 4.1
Set equal to .
Step 4.2
Solve for .
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Step 4.2.1
Add and .
Step 4.2.2
Subtract from both sides of the equation.
Step 4.2.3
Divide each term in by and simplify.
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Step 4.2.3.1
Divide each term in by .
Step 4.2.3.2
Simplify the left side.
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Step 4.2.3.2.1
Cancel the common factor of .
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Step 4.2.3.2.1.1
Cancel the common factor.
Step 4.2.3.2.1.2
Divide by .
Step 4.2.3.3
Simplify the right side.
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Step 4.2.3.3.1
Move the negative in front of the fraction.
Step 5
The final solution is all the values that make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: