Basic Math Examples

Solve for y (9y+5)(2y^2-17y-9)=0
(9y+5)(2y2-17y-9)=0(9y+5)(2y217y9)=0
Step 1
If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.
9y+5=09y+5=0
2y2-17y-9=02y217y9=0
Step 2
Set 9y+59y+5 equal to 00 and solve for yy.
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Step 2.1
Set 9y+59y+5 equal to 00.
9y+5=09y+5=0
Step 2.2
Solve 9y+5=09y+5=0 for yy.
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Step 2.2.1
Subtract 55 from both sides of the equation.
9y=-59y=5
Step 2.2.2
Divide each term in 9y=-59y=5 by 99 and simplify.
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Step 2.2.2.1
Divide each term in 9y=-59y=5 by 99.
9y9=-599y9=59
Step 2.2.2.2
Simplify the left side.
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Step 2.2.2.2.1
Cancel the common factor of 99.
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Step 2.2.2.2.1.1
Cancel the common factor.
9y9=-59
Step 2.2.2.2.1.2
Divide y by 1.
y=-59
y=-59
y=-59
Step 2.2.2.3
Simplify the right side.
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Step 2.2.2.3.1
Move the negative in front of the fraction.
y=-59
y=-59
y=-59
y=-59
y=-59
Step 3
Set 2y2-17y-9 equal to 0 and solve for y.
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Step 3.1
Set 2y2-17y-9 equal to 0.
2y2-17y-9=0
Step 3.2
Solve 2y2-17y-9=0 for y.
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Step 3.2.1
Factor by grouping.
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Step 3.2.1.1
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is ac=2-9=-18 and whose sum is b=-17.
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Step 3.2.1.1.1
Factor -17 out of -17y.
2y2-17y-9=0
Step 3.2.1.1.2
Rewrite -17 as 1 plus -18
2y2+(1-18)y-9=0
Step 3.2.1.1.3
Apply the distributive property.
2y2+1y-18y-9=0
Step 3.2.1.1.4
Multiply y by 1.
2y2+y-18y-9=0
2y2+y-18y-9=0
Step 3.2.1.2
Factor out the greatest common factor from each group.
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Step 3.2.1.2.1
Group the first two terms and the last two terms.
(2y2+y)-18y-9=0
Step 3.2.1.2.2
Factor out the greatest common factor (GCF) from each group.
y(2y+1)-9(2y+1)=0
y(2y+1)-9(2y+1)=0
Step 3.2.1.3
Factor the polynomial by factoring out the greatest common factor, 2y+1.
(2y+1)(y-9)=0
(2y+1)(y-9)=0
Step 3.2.2
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2y+1=0
y-9=0
Step 3.2.3
Set 2y+1 equal to 0 and solve for y.
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Step 3.2.3.1
Set 2y+1 equal to 0.
2y+1=0
Step 3.2.3.2
Solve 2y+1=0 for y.
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Step 3.2.3.2.1
Subtract 1 from both sides of the equation.
2y=-1
Step 3.2.3.2.2
Divide each term in 2y=-1 by 2 and simplify.
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Step 3.2.3.2.2.1
Divide each term in 2y=-1 by 2.
2y2=-12
Step 3.2.3.2.2.2
Simplify the left side.
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Step 3.2.3.2.2.2.1
Cancel the common factor of 2.
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Step 3.2.3.2.2.2.1.1
Cancel the common factor.
2y2=-12
Step 3.2.3.2.2.2.1.2
Divide y by 1.
y=-12
y=-12
y=-12
Step 3.2.3.2.2.3
Simplify the right side.
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Step 3.2.3.2.2.3.1
Move the negative in front of the fraction.
y=-12
y=-12
y=-12
y=-12
y=-12
Step 3.2.4
Set y-9 equal to 0 and solve for y.
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Step 3.2.4.1
Set y-9 equal to 0.
y-9=0
Step 3.2.4.2
Add 9 to both sides of the equation.
y=9
y=9
Step 3.2.5
The final solution is all the values that make (2y+1)(y-9)=0 true.
y=-12,9
y=-12,9
y=-12,9
Step 4
The final solution is all the values that make (9y+5)(2y2-17y-9)=0 true.
y=-59,-12,9
Step 5
The result can be shown in multiple forms.
Exact Form:
y=-59,-12,9
Decimal Form:
y=-0.5,-0.5,9
 [x2  12  π  xdx ]