3(t-5)(t-9)=-2(t-11)(t-11)

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Solution for 3(t-5)(t-9)=-2(t-11)(t-11) equation: 


Simplifying
3(t + -5)(t + -9) = -2(t + -11)(t + -11)

Reorder the terms:
3(-5 + t)(t + -9) = -2(t + -11)(t + -11)

Reorder the terms:
3(-5 + t)(-9 + t) = -2(t + -11)(t + -11)

Multiply (-5 + t) * (-9 + t)
3(-5(-9 + t) + t(-9 + t)) = -2(t + -11)(t + -11)
3((-9 * -5 + t * -5) + t(-9 + t)) = -2(t + -11)(t + -11)
3((45 + -5t) + t(-9 + t)) = -2(t + -11)(t + -11)
3(45 + -5t + (-9 * t + t * t)) = -2(t + -11)(t + -11)
3(45 + -5t + (-9t + t2)) = -2(t + -11)(t + -11)

Combine like terms: -5t + -9t = -14t
3(45 + -14t + t2) = -2(t + -11)(t + -11)
(45 * 3 + -14t * 3 + t2 * 3) = -2(t + -11)(t + -11)
(135 + -42t + 3t2) = -2(t + -11)(t + -11)

Reorder the terms:
135 + -42t + 3t2 = -2(-11 + t)(t + -11)

Reorder the terms:
135 + -42t + 3t2 = -2(-11 + t)(-11 + t)

Multiply (-11 + t) * (-11 + t)
135 + -42t + 3t2 = -2(-11(-11 + t) + t(-11 + t))
135 + -42t + 3t2 = -2((-11 * -11 + t * -11) + t(-11 + t))
135 + -42t + 3t2 = -2((121 + -11t) + t(-11 + t))
135 + -42t + 3t2 = -2(121 + -11t + (-11 * t + t * t))
135 + -42t + 3t2 = -2(121 + -11t + (-11t + t2))

Combine like terms: -11t + -11t = -22t
135 + -42t + 3t2 = -2(121 + -22t + t2)
135 + -42t + 3t2 = (121 * -2 + -22t * -2 + t2 * -2)
135 + -42t + 3t2 = (-242 + 44t + -2t2)

Solving
135 + -42t + 3t2 = -242 + 44t + -2t2

Solving for variable 't'.

Reorder the terms:
135 + 242 + -42t + -44t + 3t2 + 2t2 = -242 + 44t + -2t2 + 242 + -44t + 2t2

Combine like terms: 135 + 242 = 377
377 + -42t + -44t + 3t2 + 2t2 = -242 + 44t + -2t2 + 242 + -44t + 2t2

Combine like terms: -42t + -44t = -86t
377 + -86t + 3t2 + 2t2 = -242 + 44t + -2t2 + 242 + -44t + 2t2

Combine like terms: 3t2 + 2t2 = 5t2
377 + -86t + 5t2 = -242 + 44t + -2t2 + 242 + -44t + 2t2

Reorder the terms:
377 + -86t + 5t2 = -242 + 242 + 44t + -44t + -2t2 + 2t2

Combine like terms: -242 + 242 = 0
377 + -86t + 5t2 = 0 + 44t + -44t + -2t2 + 2t2
377 + -86t + 5t2 = 44t + -44t + -2t2 + 2t2

Combine like terms: 44t + -44t = 0
377 + -86t + 5t2 = 0 + -2t2 + 2t2
377 + -86t + 5t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
377 + -86t + 5t2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
75.4 + -17.2t + t2 = 0

Move the constant term to the right:

Add '-75.4' to each side of the equation.
75.4 + -17.2t + -75.4 + t2 = 0 + -75.4

Reorder the terms:
75.4 + -75.4 + -17.2t + t2 = 0 + -75.4

Combine like terms: 75.4 + -75.4 = 0.0
0.0 + -17.2t + t2 = 0 + -75.4
-17.2t + t2 = 0 + -75.4

Combine like terms: 0 + -75.4 = -75.4
-17.2t + t2 = -75.4

The t term is -17.2t.  Take half its coefficient (-8.6).
Square it (73.96) and add it to both sides.

Add '73.96' to each side of the equation.
-17.2t + 73.96 + t2 = -75.4 + 73.96

Reorder the terms:
73.96 + -17.2t + t2 = -75.4 + 73.96

Combine like terms: -75.4 + 73.96 = -1.44
73.96 + -17.2t + t2 = -1.44

Factor a perfect square on the left side:
(t + -8.6)(t + -8.6) = -1.44

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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