(2x+5)x(7x-2)=(4x+3)x(5x-1)+82

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Solution for (2x+5)x(7x-2)=(4x+3)x(5x-1)+82 equation: 


Simplifying
(2x + 5) * x(7x + -2) = (4x + 3) * x(5x + -1) + 82

Reorder the terms:
(5 + 2x) * x(7x + -2) = (4x + 3) * x(5x + -1) + 82

Reorder the terms:
(5 + 2x) * x(-2 + 7x) = (4x + 3) * x(5x + -1) + 82

Reorder the terms for easier multiplication:
x(5 + 2x)(-2 + 7x) = (4x + 3) * x(5x + -1) + 82

Multiply (5 + 2x) * (-2 + 7x)
x(5(-2 + 7x) + 2x * (-2 + 7x)) = (4x + 3) * x(5x + -1) + 82
x((-2 * 5 + 7x * 5) + 2x * (-2 + 7x)) = (4x + 3) * x(5x + -1) + 82
x((-10 + 35x) + 2x * (-2 + 7x)) = (4x + 3) * x(5x + -1) + 82
x(-10 + 35x + (-2 * 2x + 7x * 2x)) = (4x + 3) * x(5x + -1) + 82
x(-10 + 35x + (-4x + 14x2)) = (4x + 3) * x(5x + -1) + 82

Combine like terms: 35x + -4x = 31x
x(-10 + 31x + 14x2) = (4x + 3) * x(5x + -1) + 82
(-10 * x + 31x * x + 14x2 * x) = (4x + 3) * x(5x + -1) + 82
(-10x + 31x2 + 14x3) = (4x + 3) * x(5x + -1) + 82

Reorder the terms:
-10x + 31x2 + 14x3 = (3 + 4x) * x(5x + -1) + 82

Reorder the terms:
-10x + 31x2 + 14x3 = (3 + 4x) * x(-1 + 5x) + 82

Reorder the terms for easier multiplication:
-10x + 31x2 + 14x3 = x(3 + 4x)(-1 + 5x) + 82

Multiply (3 + 4x) * (-1 + 5x)
-10x + 31x2 + 14x3 = x(3(-1 + 5x) + 4x * (-1 + 5x)) + 82
-10x + 31x2 + 14x3 = x((-1 * 3 + 5x * 3) + 4x * (-1 + 5x)) + 82
-10x + 31x2 + 14x3 = x((-3 + 15x) + 4x * (-1 + 5x)) + 82
-10x + 31x2 + 14x3 = x(-3 + 15x + (-1 * 4x + 5x * 4x)) + 82
-10x + 31x2 + 14x3 = x(-3 + 15x + (-4x + 20x2)) + 82

Combine like terms: 15x + -4x = 11x
-10x + 31x2 + 14x3 = x(-3 + 11x + 20x2) + 82
-10x + 31x2 + 14x3 = (-3 * x + 11x * x + 20x2 * x) + 82
-10x + 31x2 + 14x3 = (-3x + 11x2 + 20x3) + 82

Reorder the terms:
-10x + 31x2 + 14x3 = 82 + -3x + 11x2 + 20x3

Solving
-10x + 31x2 + 14x3 = 82 + -3x + 11x2 + 20x3

Solving for variable 'x'.

Reorder the terms:
-82 + -10x + 3x + 31x2 + -11x2 + 14x3 + -20x3 = 82 + -3x + 11x2 + 20x3 + -82 + 3x + -11x2 + -20x3

Combine like terms: -10x + 3x = -7x
-82 + -7x + 31x2 + -11x2 + 14x3 + -20x3 = 82 + -3x + 11x2 + 20x3 + -82 + 3x + -11x2 + -20x3

Combine like terms: 31x2 + -11x2 = 20x2
-82 + -7x + 20x2 + 14x3 + -20x3 = 82 + -3x + 11x2 + 20x3 + -82 + 3x + -11x2 + -20x3

Combine like terms: 14x3 + -20x3 = -6x3
-82 + -7x + 20x2 + -6x3 = 82 + -3x + 11x2 + 20x3 + -82 + 3x + -11x2 + -20x3

Reorder the terms:
-82 + -7x + 20x2 + -6x3 = 82 + -82 + -3x + 3x + 11x2 + -11x2 + 20x3 + -20x3

Combine like terms: 82 + -82 = 0
-82 + -7x + 20x2 + -6x3 = 0 + -3x + 3x + 11x2 + -11x2 + 20x3 + -20x3
-82 + -7x + 20x2 + -6x3 = -3x + 3x + 11x2 + -11x2 + 20x3 + -20x3

Combine like terms: -3x + 3x = 0
-82 + -7x + 20x2 + -6x3 = 0 + 11x2 + -11x2 + 20x3 + -20x3
-82 + -7x + 20x2 + -6x3 = 11x2 + -11x2 + 20x3 + -20x3

Combine like terms: 11x2 + -11x2 = 0
-82 + -7x + 20x2 + -6x3 = 0 + 20x3 + -20x3
-82 + -7x + 20x2 + -6x3 = 20x3 + -20x3

Combine like terms: 20x3 + -20x3 = 0
-82 + -7x + 20x2 + -6x3 = 0

The solution to this equation could not be determined.

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