# Solve for y y^3-64=0 y3-64=0
Add 64 to both sides of the equation.
y3=64
Move 64 to the left side of the equation by subtracting it from both sides.
y3-64=0
Factor the left side of the equation.
Rewrite 64 as 43.
y3-43=0
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=y and b=4.
(y-4)(y2+y⋅4+42)=0
Simplify.
Move 4 to the left of y.
(y-4)(y2+4y+42)=0
Raise 4 to the power of 2.
(y-4)(y2+4y+16)=0
(y-4)(y2+4y+16)=0
(y-4)(y2+4y+16)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y-4=0
y2+4y+16=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
y-4=0
Add 4 to both sides of the equation.
y=4
y=4
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
y2+4y+16=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=4, and c=16 into the quadratic formula and solve for y.
-4±42-4⋅(1⋅16)2⋅1
Simplify.
Simplify the numerator.
Raise 4 to the power of 2.
y=-4±16-4⋅(1⋅16)2⋅1
Multiply 16 by 1.
y=-4±16-4⋅162⋅1
Multiply -4 by 16.
y=-4±16-642⋅1
Subtract 64 from 16.
y=-4±-482⋅1
Rewrite -48 as -1(48).
y=-4±-1⋅482⋅1
Rewrite -1(48) as -1⋅48.
y=-4±-1⋅482⋅1
Rewrite -1 as i.
y=-4±i⋅482⋅1
Rewrite 48 as 42⋅3.
Factor 16 out of 48.
y=-4±i⋅16(3)2⋅1
Rewrite 16 as 42.
y=-4±i⋅42⋅32⋅1
y=-4±i⋅42⋅32⋅1
Pull terms out from under the radical.
y=-4±i⋅(43)2⋅1
Move 4 to the left of i.
y=-4±4i32⋅1
y=-4±4i32⋅1
Multiply 2 by 1.
y=-4±4i32
Simplify -4±4i32.
y=-2±2i3
y=-2±2i3
The final answer is the combination of both solutions.
y=-2+2i3,-2-2i3
y=-2+2i3,-2-2i3
The final solution is all the values that make (y-4)(y2+4y+16)=0 true.
y=4,-2+2i3,-2-2i3
Solve for y y^3-64=0

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