To solve this equation, we first need to distribute the terms on both sides of the equation:
24 - (3y + 1)(4y - 5) = (11 - 6y)(2y - 1) + 6
Expanding the expressions:
24 - 12y^2 + 15y - 4y + 5 = 22y^2 - 11y - 6y + 3 + 6
Simplify the equation:
24 - 12y^2 + 11y + 5 = 22y^2 - 17y - 3 + 6
Combine like terms:
29 - 12y^2 + 11y = 22y^2 - 17y + 3
Rearranging the equation:
29 = 22y^2 - 17y + 3 + 12y^2 - 11y
29 = 34y^2 - 28y + 3
34y^2 - 28y - 29 = 0
This is a quadratic equation, and we can solve this using the quadratic formula:
y = (-(-28) ± sqrt((-28)^2 - 434-29)) / 2*34y = (28 ± sqrt(784 + 3944)) / 68y = (28 ± sqrt(4728)) / 68y ≈ (28 ± 68.77) / 68
Therefore, the solutions for y are:
y ≈ 1.39 or y ≈ -1.07
To solve this equation, we first need to distribute the terms on both sides of the equation:
24 - (3y + 1)(4y - 5) = (11 - 6y)(2y - 1) + 6
Expanding the expressions:
24 - 12y^2 + 15y - 4y + 5 = 22y^2 - 11y - 6y + 3 + 6
Simplify the equation:
24 - 12y^2 + 11y + 5 = 22y^2 - 17y - 3 + 6
Combine like terms:
29 - 12y^2 + 11y = 22y^2 - 17y + 3
Rearranging the equation:
29 = 22y^2 - 17y + 3 + 12y^2 - 11y
Combine like terms:
29 = 34y^2 - 28y + 3
Rearranging the equation:
34y^2 - 28y - 29 = 0
This is a quadratic equation, and we can solve this using the quadratic formula:
y = (-(-28) ± sqrt((-28)^2 - 434-29)) / 2*34
y = (28 ± sqrt(784 + 3944)) / 68
y = (28 ± sqrt(4728)) / 68
y ≈ (28 ± 68.77) / 68
Therefore, the solutions for y are:
y ≈ 1.39 or y ≈ -1.07