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

y(y+6)=-32
Simplify y(y+6).
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.
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

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