Solve for z 9z^2-12zy+4y^2=0

Math
9z2-12zy+4y2=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=9, b=-12y, and c=4y2 into the quadratic formula and solve for z.
12y±(-12y)2-4⋅(9⋅(4y2))2⋅9
Simplify.
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Simplify the numerator.
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Rewrite 4⋅(9⋅(4y2)) as (2⋅(3⋅(2y)))2.
z=12y±(-12y)2-(2⋅(3⋅(2y)))22⋅9
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=-12y and b=2⋅(3⋅(2y)).
z=12y±(-12y+2⋅(3⋅(2y)))(-12y-(2⋅(3⋅(2y))))2⋅9
Simplify.
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Factor 2y out of -12y+2⋅(3⋅(2y)).
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Factor 2y out of -12y.
z=12y±(2y(-6)+2⋅(3⋅(2y)))(-12y-(2⋅(3⋅(2y))))2⋅9
Factor 2y out of 2⋅(3⋅(2y)).
z=12y±(2y(-6)+2y(3⋅(2)))(-12y-(2⋅(3⋅(2y))))2⋅9
Factor 2y out of 2y(-6)+2y(3⋅(2)).
z=12y±2y(-6+3⋅(2))(-12y-(2⋅(3⋅(2y))))2⋅9
z=12y±2y(-6+3⋅(2))(-12y-(2⋅(3⋅(2y))))2⋅9
Multiply 3 by 2.
z=12y±2y(-6+6)(-12y-(2⋅(3⋅(2y))))2⋅9
Combine exponents.
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Multiply 2 by 3.
z=12y±2y(-6+6)(-12y-(2⋅(6⋅y)))2⋅9
Multiply 6 by 2.
z=12y±2y(-6+6)(-12y-(12⋅y))2⋅9
Multiply 12 by -1.
z=12y±2y(-6+6)(-12y-12y)2⋅9
z=12y±2y(-6+6)(-12y-12y)2⋅9
z=12y±2y(-6+6)(-12y-12y)2⋅9
Add -6 and 6.
z=12y±2y⋅(0(-12y-12y))2⋅9
Subtract 12y from -12y.
z=12y±2y⋅(0(-24y))2⋅9
Multiply 0 by 2.
z=12y±0y⋅(-24y)2⋅9
Multiply 0 by y.
z=12y±0⋅(-24y)2⋅9
Multiply 0 by -24.
z=12y±0y2⋅9
Multiply 0 by y.
z=12y±02⋅9
Rewrite 0 as 02.
z=12y±022⋅9
Pull terms out from under the radical, assuming positive real numbers.
z=12y±02⋅9
z=12y±02⋅9
Multiply 2 by 9.
z=12y±018
Simplify 12y±018.
z=12y18
Cancel the common factor of 12 and 18.
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Factor 6 out of 12y.
z=6(2y)18
Cancel the common factors.
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Factor 6 out of 18.
z=6(2y)6(3)
Cancel the common factor.
z=6(2y)6⋅3
Rewrite the expression.
z=2y3
z=2y3
z=2y3
z=2y3
The final answer is the combination of both solutions.
z=2y3 Double roots
Solve for z 9z^2-12zy+4y^2=0

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