(5y+11)(2y+12)-(13y+10)(5y+11)=0

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Solution for (5y+11)(2y+12)-(13y+10)(5y+11)=0 equation:


Simplifying
(5y + 11)(2y + 12) + -1(13y + 10)(5y + 11) = 0

Reorder the terms:
(11 + 5y)(2y + 12) + -1(13y + 10)(5y + 11) = 0

Reorder the terms:
(11 + 5y)(12 + 2y) + -1(13y + 10)(5y + 11) = 0

Multiply (11 + 5y) * (12 + 2y)
(11(12 + 2y) + 5y * (12 + 2y)) + -1(13y + 10)(5y + 11) = 0
((12 * 11 + 2y * 11) + 5y * (12 + 2y)) + -1(13y + 10)(5y + 11) = 0
((132 + 22y) + 5y * (12 + 2y)) + -1(13y + 10)(5y + 11) = 0
(132 + 22y + (12 * 5y + 2y * 5y)) + -1(13y + 10)(5y + 11) = 0
(132 + 22y + (60y + 10y2)) + -1(13y + 10)(5y + 11) = 0

Combine like terms: 22y + 60y = 82y
(132 + 82y + 10y2) + -1(13y + 10)(5y + 11) = 0

Reorder the terms:
132 + 82y + 10y2 + -1(10 + 13y)(5y + 11) = 0

Reorder the terms:
132 + 82y + 10y2 + -1(10 + 13y)(11 + 5y) = 0

Multiply (10 + 13y) * (11 + 5y)
132 + 82y + 10y2 + -1(10(11 + 5y) + 13y * (11 + 5y)) = 0
132 + 82y + 10y2 + -1((11 * 10 + 5y * 10) + 13y * (11 + 5y)) = 0
132 + 82y + 10y2 + -1((110 + 50y) + 13y * (11 + 5y)) = 0
132 + 82y + 10y2 + -1(110 + 50y + (11 * 13y + 5y * 13y)) = 0
132 + 82y + 10y2 + -1(110 + 50y + (143y + 65y2)) = 0

Combine like terms: 50y + 143y = 193y
132 + 82y + 10y2 + -1(110 + 193y + 65y2) = 0
132 + 82y + 10y2 + (110 * -1 + 193y * -1 + 65y2 * -1) = 0
132 + 82y + 10y2 + (-110 + -193y + -65y2) = 0

Reorder the terms:
132 + -110 + 82y + -193y + 10y2 + -65y2 = 0

Combine like terms: 132 + -110 = 22
22 + 82y + -193y + 10y2 + -65y2 = 0

Combine like terms: 82y + -193y = -111y
22 + -111y + 10y2 + -65y2 = 0

Combine like terms: 10y2 + -65y2 = -55y2
22 + -111y + -55y2 = 0

Solving
22 + -111y + -55y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + -11y)(11 + 5y) = 0

Subproblem 1

Set the factor '(2 + -11y)' equal to zero and attempt to solve: Simplifying 2 + -11y = 0 Solving 2 + -11y = 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 + -11y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -11y = 0 + -2 -11y = 0 + -2 Combine like terms: 0 + -2 = -2 -11y = -2 Divide each side by '-11'. y = 0.1818181818 Simplifying y = 0.1818181818

Subproblem 2

Set the factor '(11 + 5y)' equal to zero and attempt to solve: Simplifying 11 + 5y = 0 Solving 11 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 5y = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 5y = 0 + -11 5y = 0 + -11 Combine like terms: 0 + -11 = -11 5y = -11 Divide each side by '5'. y = -2.2 Simplifying y = -2.2

Solution

y = {0.1818181818, -2.2}

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