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Simplifying (7 + 7y)(6y + 1) = 0 Reorder the terms: (7 + 7y)(1 + 6y) = 0 Multiply (7 + 7y) * (1 + 6y) (7(1 + 6y) + 7y * (1 + 6y)) = 0 ((1 * 7 + 6y * 7) + 7y * (1 + 6y)) = 0 ((7 + 42y) + 7y * (1 + 6y)) = 0 (7 + 42y + (1 * 7y + 6y * 7y)) = 0 (7 + 42y + (7y + 42y2)) = 0 Combine like terms: 42y + 7y = 49y (7 + 49y + 42y2) = 0 Solving 7 + 49y + 42y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7'. 7(1 + 7y + 6y2) = 0 Factor a trinomial. 7((1 + y)(1 + 6y)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Subproblem 2
Set the factor '(1 + 6y)' equal to zero and attempt to solve: Simplifying 1 + 6y = 0 Solving 1 + 6y = 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 + 6y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6y = 0 + -1 6y = 0 + -1 Combine like terms: 0 + -1 = -1 6y = -1 Divide each side by '6'. y = -0.1666666667 Simplifying y = -0.1666666667Solution
y = {-1, -0.1666666667}
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