23y(y-4)(y-13)=0

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Solution for 23y(y-4)(y-13)=0 equation: 


Simplifying
23y(y + -4)(y + -13) = 0

Reorder the terms:
23y(-4 + y)(y + -13) = 0

Reorder the terms:
23y(-4 + y)(-13 + y) = 0

Multiply (-4 + y) * (-13 + y)
23y(-4(-13 + y) + y(-13 + y)) = 0
23y((-13 * -4 + y * -4) + y(-13 + y)) = 0
23y((52 + -4y) + y(-13 + y)) = 0
23y(52 + -4y + (-13 * y + y * y)) = 0
23y(52 + -4y + (-13y + y2)) = 0

Combine like terms: -4y + -13y = -17y
23y(52 + -17y + y2) = 0
(52 * 23y + -17y * 23y + y2 * 23y) = 0
(1196y + -391y2 + 23y3) = 0

Solving
1196y + -391y2 + 23y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '23y'.
23y(52 + -17y + y2) = 0

Factor a trinomial.
23y((4 + -1y)(13 + -1y)) = 0

Ignore the factor 23.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

Move all terms containing y to the left, all other terms to the right.

Simplifying
y = 0

Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4

Subproblem 3
Set the factor '(13 + -1y)' equal to zero and attempt to solve:

Simplifying
13 + -1y = 0

Solving
13 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-13' to each side of the equation.
13 + -13 + -1y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1y = 0 + -13
-1y = 0 + -13

Combine like terms: 0 + -13 = -13
-1y = -13

Divide each side by '-1'.
y = 13

Simplifying
y = 13
Solution
y = {0, 4, 13}

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