Basic Math Examples

Solve for a 3a-2=27a^3-18a^2
Step 1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
Subtract from both sides of the equation.
Step 3
Add to both sides of the equation.
Step 4
Factor the left side of the equation.
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Step 4.1
Factor out the greatest common factor from each group.
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Step 4.1.1
Group the first two terms and the last two terms.
Step 4.1.2
Factor out the greatest common factor (GCF) from each group.
Step 4.2
Factor the polynomial by factoring out the greatest common factor, .
Step 4.3
Rewrite as .
Step 4.4
Rewrite as .
Step 4.5
Factor.
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Step 4.5.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 4.5.2
Remove unnecessary parentheses.
Step 5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Solve for .
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Step 6.2.1
Add to both sides of the equation.
Step 6.2.2
Divide each term in by and simplify.
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Step 6.2.2.1
Divide each term in by .
Step 6.2.2.2
Simplify the left side.
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Step 6.2.2.2.1
Cancel the common factor of .
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Step 6.2.2.2.1.1
Cancel the common factor.
Step 6.2.2.2.1.2
Divide by .
Step 7
Set equal to and solve for .
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Step 7.1
Set equal to .
Step 7.2
Solve for .
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Step 7.2.1
Subtract from both sides of the equation.
Step 7.2.2
Divide each term in by and simplify.
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Step 7.2.2.1
Divide each term in by .
Step 7.2.2.2
Simplify the left side.
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Step 7.2.2.2.1
Cancel the common factor of .
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Step 7.2.2.2.1.1
Cancel the common factor.
Step 7.2.2.2.1.2
Divide by .
Step 7.2.2.3
Simplify the right side.
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Step 7.2.2.3.1
Move the negative in front of the fraction.
Step 8
Set equal to and solve for .
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Step 8.1
Set equal to .
Step 8.2
Solve for .
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Step 8.2.1
Add to both sides of the equation.
Step 8.2.2
Divide each term in by and simplify.
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Step 8.2.2.1
Divide each term in by .
Step 8.2.2.2
Simplify the left side.
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Step 8.2.2.2.1
Cancel the common factor of .
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Step 8.2.2.2.1.1
Cancel the common factor.
Step 8.2.2.2.1.2
Divide by .
Step 9
The final solution is all the values that make true.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: