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Simplifying (3y + 12)(10y + 11) + (6y + 13)(3y + 12) = 0 Reorder the terms: (12 + 3y)(10y + 11) + (6y + 13)(3y + 12) = 0 Reorder the terms: (12 + 3y)(11 + 10y) + (6y + 13)(3y + 12) = 0 Multiply (12 + 3y) * (11 + 10y) (12(11 + 10y) + 3y * (11 + 10y)) + (6y + 13)(3y + 12) = 0 ((11 * 12 + 10y * 12) + 3y * (11 + 10y)) + (6y + 13)(3y + 12) = 0 ((132 + 120y) + 3y * (11 + 10y)) + (6y + 13)(3y + 12) = 0 (132 + 120y + (11 * 3y + 10y * 3y)) + (6y + 13)(3y + 12) = 0 (132 + 120y + (33y + 30y2)) + (6y + 13)(3y + 12) = 0 Combine like terms: 120y + 33y = 153y (132 + 153y + 30y2) + (6y + 13)(3y + 12) = 0 Reorder the terms: 132 + 153y + 30y2 + (13 + 6y)(3y + 12) = 0 Reorder the terms: 132 + 153y + 30y2 + (13 + 6y)(12 + 3y) = 0 Multiply (13 + 6y) * (12 + 3y) 132 + 153y + 30y2 + (13(12 + 3y) + 6y * (12 + 3y)) = 0 132 + 153y + 30y2 + ((12 * 13 + 3y * 13) + 6y * (12 + 3y)) = 0 132 + 153y + 30y2 + ((156 + 39y) + 6y * (12 + 3y)) = 0 132 + 153y + 30y2 + (156 + 39y + (12 * 6y + 3y * 6y)) = 0 132 + 153y + 30y2 + (156 + 39y + (72y + 18y2)) = 0 Combine like terms: 39y + 72y = 111y 132 + 153y + 30y2 + (156 + 111y + 18y2) = 0 Reorder the terms: 132 + 156 + 153y + 111y + 30y2 + 18y2 = 0 Combine like terms: 132 + 156 = 288 288 + 153y + 111y + 30y2 + 18y2 = 0 Combine like terms: 153y + 111y = 264y 288 + 264y + 30y2 + 18y2 = 0 Combine like terms: 30y2 + 18y2 = 48y2 288 + 264y + 48y2 = 0 Solving 288 + 264y + 48y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '24'. 24(12 + 11y + 2y2) = 0 Factor a trinomial. 24((4 + y)(3 + 2y)) = 0 Ignore the factor 24.Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve: Simplifying 4 + y = 0 Solving 4 + y = 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 + y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y = 0 + -4 y = 0 + -4 Combine like terms: 0 + -4 = -4 y = -4 Simplifying y = -4Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Divide each side by '2'. y = -1.5 Simplifying y = -1.5Solution
y = {-4, -1.5}
| 2/6=y | | -19+4(23/3)=35/3 | | (12a+11)(4a+10)=0 | | 91/13=z | | (10y+4)(13y+5)+(7y+8)(10y+4)=0 | | -19+4y=35/3 | | 54/9=x | | 1/3*-57 | | 12x+13=2x+15 | | 10y+6=8y+7 | | (-19/60)/(1/180) | | x=2+215y | | 11b+12=15+8b | | m+.21m=15049 | | 2+10z=15z+9 | | (3a+13)(9a+15)-(11a+7)(3a+13)=0 | | 10+5a=4+2a | | (10a+2)(12a+9)=0 | | (10b+2)(12a+9)=0 | | 5x-10y=55 | | 13+6y=14y+10 | | (35/3)/4 | | (1/3)/4 | | 6r^5-9r^4=0 | | p-.35p=75.68 | | 8w^2=30+34w | | 9+5x=3+18x | | -43/18+253/360 | | 3+12y=2y+9 | | 1/5*253/72 | | 13z+5=8z+11 | | -43/18+253/18 |