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Simplifying (4y + 1)(7y + -14) = 0 Reorder the terms: (1 + 4y)(7y + -14) = 0 Reorder the terms: (1 + 4y)(-14 + 7y) = 0 Multiply (1 + 4y) * (-14 + 7y) (1(-14 + 7y) + 4y * (-14 + 7y)) = 0 ((-14 * 1 + 7y * 1) + 4y * (-14 + 7y)) = 0 ((-14 + 7y) + 4y * (-14 + 7y)) = 0 (-14 + 7y + (-14 * 4y + 7y * 4y)) = 0 (-14 + 7y + (-56y + 28y2)) = 0 Combine like terms: 7y + -56y = -49y (-14 + -49y + 28y2) = 0 Solving -14 + -49y + 28y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7'. 7(-2 + -7y + 4y2) = 0 Factor a trinomial. 7((-1 + -4y)(2 + -1y)) = 0 Ignore the factor 7.Subproblem 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 '(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 = 2Solution
y = {-0.25, 2}
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