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Simplifying (3y + 1)(4y + -5) + -1(6y + -11)(2y + -7) = 24 Reorder the terms: (1 + 3y)(4y + -5) + -1(6y + -11)(2y + -7) = 24 Reorder the terms: (1 + 3y)(-5 + 4y) + -1(6y + -11)(2y + -7) = 24 Multiply (1 + 3y) * (-5 + 4y) (1(-5 + 4y) + 3y * (-5 + 4y)) + -1(6y + -11)(2y + -7) = 24 ((-5 * 1 + 4y * 1) + 3y * (-5 + 4y)) + -1(6y + -11)(2y + -7) = 24 ((-5 + 4y) + 3y * (-5 + 4y)) + -1(6y + -11)(2y + -7) = 24 (-5 + 4y + (-5 * 3y + 4y * 3y)) + -1(6y + -11)(2y + -7) = 24 (-5 + 4y + (-15y + 12y2)) + -1(6y + -11)(2y + -7) = 24 Combine like terms: 4y + -15y = -11y (-5 + -11y + 12y2) + -1(6y + -11)(2y + -7) = 24 Reorder the terms: -5 + -11y + 12y2 + -1(-11 + 6y)(2y + -7) = 24 Reorder the terms: -5 + -11y + 12y2 + -1(-11 + 6y)(-7 + 2y) = 24 Multiply (-11 + 6y) * (-7 + 2y) -5 + -11y + 12y2 + -1(-11(-7 + 2y) + 6y * (-7 + 2y)) = 24 -5 + -11y + 12y2 + -1((-7 * -11 + 2y * -11) + 6y * (-7 + 2y)) = 24 -5 + -11y + 12y2 + -1((77 + -22y) + 6y * (-7 + 2y)) = 24 -5 + -11y + 12y2 + -1(77 + -22y + (-7 * 6y + 2y * 6y)) = 24 -5 + -11y + 12y2 + -1(77 + -22y + (-42y + 12y2)) = 24 Combine like terms: -22y + -42y = -64y -5 + -11y + 12y2 + -1(77 + -64y + 12y2) = 24 -5 + -11y + 12y2 + (77 * -1 + -64y * -1 + 12y2 * -1) = 24 -5 + -11y + 12y2 + (-77 + 64y + -12y2) = 24 Reorder the terms: -5 + -77 + -11y + 64y + 12y2 + -12y2 = 24 Combine like terms: -5 + -77 = -82 -82 + -11y + 64y + 12y2 + -12y2 = 24 Combine like terms: -11y + 64y = 53y -82 + 53y + 12y2 + -12y2 = 24 Combine like terms: 12y2 + -12y2 = 0 -82 + 53y + 0 = 24 -82 + 53y = 24 Solving -82 + 53y = 24 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '82' to each side of the equation. -82 + 82 + 53y = 24 + 82 Combine like terms: -82 + 82 = 0 0 + 53y = 24 + 82 53y = 24 + 82 Combine like terms: 24 + 82 = 106 53y = 106 Divide each side by '53'. y = 2 Simplifying y = 2
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