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Simplifying (-1 + 4y)(-4 + y) = 0 Multiply (-1 + 4y) * (-4 + y) (-1(-4 + y) + 4y * (-4 + y)) = 0 ((-4 * -1 + y * -1) + 4y * (-4 + y)) = 0 ((4 + -1y) + 4y * (-4 + y)) = 0 (4 + -1y + (-4 * 4y + y * 4y)) = 0 (4 + -1y + (-16y + 4y2)) = 0 Combine like terms: -1y + -16y = -17y (4 + -17y + 4y2) = 0 Solving 4 + -17y + 4y2 = 0 Solving for variable 'y'. Factor a trinomial. (1 + -4y)(4 + -1y) = 0Subproblem 1
Set the factor '(1 + -4y)' equal to zero and attempt to solve: Simplifying 1 + -4y = 0 Solving 1 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4y = 0 + -1 -4y = 0 + -1 Combine like terms: 0 + -1 = -1 -4y = -1 Divide each side by '-4'. y = 0.25 Simplifying y = 0.25Subproblem 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 = 4Solution
y = {0.25, 4}
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