2(-x+11)(3x+4)=5(-x+11)(x-6)

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Solution for 2(-x+11)(3x+4)=5(-x+11)(x-6) equation: 


Simplifying
2(-1x + 11)(3x + 4) = 5(-1x + 11)(x + -6)

Reorder the terms:
2(11 + -1x)(3x + 4) = 5(-1x + 11)(x + -6)

Reorder the terms:
2(11 + -1x)(4 + 3x) = 5(-1x + 11)(x + -6)

Multiply (11 + -1x) * (4 + 3x)
2(11(4 + 3x) + -1x * (4 + 3x)) = 5(-1x + 11)(x + -6)
2((4 * 11 + 3x * 11) + -1x * (4 + 3x)) = 5(-1x + 11)(x + -6)
2((44 + 33x) + -1x * (4 + 3x)) = 5(-1x + 11)(x + -6)
2(44 + 33x + (4 * -1x + 3x * -1x)) = 5(-1x + 11)(x + -6)
2(44 + 33x + (-4x + -3x2)) = 5(-1x + 11)(x + -6)

Combine like terms: 33x + -4x = 29x
2(44 + 29x + -3x2) = 5(-1x + 11)(x + -6)
(44 * 2 + 29x * 2 + -3x2 * 2) = 5(-1x + 11)(x + -6)
(88 + 58x + -6x2) = 5(-1x + 11)(x + -6)

Reorder the terms:
88 + 58x + -6x2 = 5(11 + -1x)(x + -6)

Reorder the terms:
88 + 58x + -6x2 = 5(11 + -1x)(-6 + x)

Multiply (11 + -1x) * (-6 + x)
88 + 58x + -6x2 = 5(11(-6 + x) + -1x * (-6 + x))
88 + 58x + -6x2 = 5((-6 * 11 + x * 11) + -1x * (-6 + x))
88 + 58x + -6x2 = 5((-66 + 11x) + -1x * (-6 + x))
88 + 58x + -6x2 = 5(-66 + 11x + (-6 * -1x + x * -1x))
88 + 58x + -6x2 = 5(-66 + 11x + (6x + -1x2))

Combine like terms: 11x + 6x = 17x
88 + 58x + -6x2 = 5(-66 + 17x + -1x2)
88 + 58x + -6x2 = (-66 * 5 + 17x * 5 + -1x2 * 5)
88 + 58x + -6x2 = (-330 + 85x + -5x2)

Solving
88 + 58x + -6x2 = -330 + 85x + -5x2

Solving for variable 'x'.

Reorder the terms:
88 + 330 + 58x + -85x + -6x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2

Combine like terms: 88 + 330 = 418
418 + 58x + -85x + -6x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2

Combine like terms: 58x + -85x = -27x
418 + -27x + -6x2 + 5x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2

Combine like terms: -6x2 + 5x2 = -1x2
418 + -27x + -1x2 = -330 + 85x + -5x2 + 330 + -85x + 5x2

Reorder the terms:
418 + -27x + -1x2 = -330 + 330 + 85x + -85x + -5x2 + 5x2

Combine like terms: -330 + 330 = 0
418 + -27x + -1x2 = 0 + 85x + -85x + -5x2 + 5x2
418 + -27x + -1x2 = 85x + -85x + -5x2 + 5x2

Combine like terms: 85x + -85x = 0
418 + -27x + -1x2 = 0 + -5x2 + 5x2
418 + -27x + -1x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
418 + -27x + -1x2 = 0

Factor a trinomial.
(11 + -1x)(38 + x) = 0


Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11

Subproblem 2
Set the factor '(38 + x)' equal to zero and attempt to solve:

Simplifying
38 + x = 0

Solving
38 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-38' to each side of the equation.
38 + -38 + x = 0 + -38

Combine like terms: 38 + -38 = 0
0 + x = 0 + -38
x = 0 + -38

Combine like terms: 0 + -38 = -38
x = -38

Simplifying
x = -38
Solution
x = {11, -38}

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