36y2-26y+46=0

Cancel the common factor of 3 and 6.

Factor 3 out of 3.

3(1)6y2-26y+46=0

Cancel the common factors.

Factor 3 out of 6.

3⋅13⋅2y2-26y+46=0

Cancel the common factor.

3⋅13⋅2y2-26y+46=0

Rewrite the expression.

12y2-26y+46=0

12y2-26y+46=0

12y2-26y+46=0

Combine 12 and y2.

y22-26y+46=0

Cancel the common factor of 2 and 6.

Factor 2 out of 2.

y22-2(1)6y+46=0

Cancel the common factors.

Factor 2 out of 6.

y22-2⋅12⋅3y+46=0

Cancel the common factor.

y22-2⋅12⋅3y+46=0

Rewrite the expression.

y22-13y+46=0

y22-13y+46=0

y22-13y+46=0

Combine y and 13.

y22-y3+46=0

Cancel the common factor of 4 and 6.

Factor 2 out of 4.

y22-y3+2(2)6=0

Cancel the common factors.

Factor 2 out of 6.

y22-y3+2⋅22⋅3=0

Cancel the common factor.

y22-y3+2⋅22⋅3=0

Rewrite the expression.

y22-y3+23=0

y22-y3+23=0

y22-y3+23=0

y22-y3+23=0

Apply the distributive property.

6(y22)+6(-y3)+6(23)=0

Simplify.

Cancel the common factor of 2.

Factor 2 out of 6.

2(3)(y22)+6(-y3)+6(23)=0

Cancel the common factor.

2⋅(3(y22))+6(-y3)+6(23)=0

Rewrite the expression.

3y2+6(-y3)+6(23)=0

3y2+6(-y3)+6(23)=0

Cancel the common factor of 3.

Move the leading negative in -y3 into the numerator.

3y2+6(-y3)+6(23)=0

Factor 3 out of 6.

3y2+3(2)(-y3)+6(23)=0

Cancel the common factor.

3y2+3⋅(2(-y3))+6(23)=0

Rewrite the expression.

3y2+2(-y)+6(23)=0

3y2+2(-y)+6(23)=0

Multiply -1 by 2.

3y2-2y+6(23)=0

Cancel the common factor of 3.

Factor 3 out of 6.

3y2-2y+3(2)(23)=0

Cancel the common factor.

3y2-2y+3⋅(2(23))=0

Rewrite the expression.

3y2-2y+2⋅2=0

3y2-2y+2⋅2=0

Multiply 2 by 2.

3y2-2y+4=0

3y2-2y+4=0

3y2-2y+4=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=3, b=-2, and c=4 into the quadratic formula and solve for y.

2±(-2)2-4⋅(3⋅4)2⋅3

Simplify the numerator.

Raise -2 to the power of 2.

y=2±4-4⋅(3⋅4)2⋅3

Multiply 3 by 4.

y=2±4-4⋅122⋅3

Multiply -4 by 12.

y=2±4-482⋅3

Subtract 48 from 4.

y=2±-442⋅3

Rewrite -44 as -1(44).

y=2±-1⋅442⋅3

Rewrite -1(44) as -1⋅44.

y=2±-1⋅442⋅3

Rewrite -1 as i.

y=2±i⋅442⋅3

Rewrite 44 as 22⋅11.

Factor 4 out of 44.

y=2±i⋅4(11)2⋅3

Rewrite 4 as 22.

y=2±i⋅22⋅112⋅3

y=2±i⋅22⋅112⋅3

Pull terms out from under the radical.

y=2±i⋅(211)2⋅3

Move 2 to the left of i.

y=2±2i112⋅3

y=2±2i112⋅3

Multiply 2 by 3.

y=2±2i116

Simplify 2±2i116.

y=1±i113

y=1±i113

The final answer is the combination of both solutions.

y=1+i113,1-i113

Solve for y 3/6y^2-2/6y+4/6=0