y(y-7)(y+2)=0

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Solution for y(y-7)(y+2)=0 equation:


Simplifying
y(y + -7)(y + 2) = 0

Reorder the terms:
y(-7 + y)(y + 2) = 0

Reorder the terms:
y(-7 + y)(2 + y) = 0

Multiply (-7 + y) * (2 + y)
y(-7(2 + y) + y(2 + y)) = 0
y((2 * -7 + y * -7) + y(2 + y)) = 0
y((-14 + -7y) + y(2 + y)) = 0
y(-14 + -7y + (2 * y + y * y)) = 0
y(-14 + -7y + (2y + y2)) = 0

Combine like terms: -7y + 2y = -5y
y(-14 + -5y + y2) = 0
(-14 * y + -5y * y + y2 * y) = 0
(-14y + -5y2 + y3) = 0

Solving
-14y + -5y2 + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-14 + -5y + y2) = 0

Factor a trinomial.
y((-2 + -1y)(7 + -1y)) = 0

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 '(-2 + -1y)' equal to zero and attempt to solve: Simplifying -2 + -1y = 0 Solving -2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1y = 0 + 2 -1y = 0 + 2 Combine like terms: 0 + 2 = 2 -1y = 2 Divide each side by '-1'. y = -2 Simplifying y = -2

Subproblem 3

Set the factor '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7

Solution

y = {0, -2, 7}

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