y(y+6)=-32

Apply the distributive property.

y⋅y+y⋅6=-32

Simplify the expression.

Multiply y by y.

y2+y⋅6=-32

Move 6 to the left of y.

y2+6y=-32

y2+6y=-32

y2+6y=-32

Move 32 to the left side of the equation by adding it to both sides.

y2+6y+32=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=6, and c=32 into the quadratic formula and solve for y.

-6±62-4⋅(1⋅32)2⋅1

Simplify the numerator.

Raise 6 to the power of 2.

y=-6±36-4⋅(1⋅32)2⋅1

Multiply 32 by 1.

y=-6±36-4⋅322⋅1

Multiply -4 by 32.

y=-6±36-1282⋅1

Subtract 128 from 36.

y=-6±-922⋅1

Rewrite -92 as -1(92).

y=-6±-1⋅922⋅1

Rewrite -1(92) as -1⋅92.

y=-6±-1⋅922⋅1

Rewrite -1 as i.

y=-6±i⋅922⋅1

Rewrite 92 as 22⋅23.

Factor 4 out of 92.

y=-6±i⋅4(23)2⋅1

Rewrite 4 as 22.

y=-6±i⋅22⋅232⋅1

y=-6±i⋅22⋅232⋅1

Pull terms out from under the radical.

y=-6±i⋅(223)2⋅1

Move 2 to the left of i.

y=-6±2i232⋅1

y=-6±2i232⋅1

Multiply 2 by 1.

y=-6±2i232

Simplify -6±2i232.

y=-3±i23

y=-3±i23

The final answer is the combination of both solutions.

y=-3+i23,-3-i23

Solve for y y(y+6)=-32