(x+1)(x+2)(2x+5)(2x+1)=45

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Solution for (x+1)(x+2)(2x+5)(2x+1)=45 equation: 


Simplifying
(x + 1)(x + 2)(2x + 5)(2x + 1) = 45

Reorder the terms:
(1 + x)(x + 2)(2x + 5)(2x + 1) = 45

Reorder the terms:
(1 + x)(2 + x)(2x + 5)(2x + 1) = 45

Reorder the terms:
(1 + x)(2 + x)(5 + 2x)(2x + 1) = 45

Reorder the terms:
(1 + x)(2 + x)(5 + 2x)(1 + 2x) = 45

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x))(5 + 2x)(1 + 2x) = 45
((2 * 1 + x * 1) + x(2 + x))(5 + 2x)(1 + 2x) = 45
((2 + 1x) + x(2 + x))(5 + 2x)(1 + 2x) = 45
(2 + 1x + (2 * x + x * x))(5 + 2x)(1 + 2x) = 45
(2 + 1x + (2x + x2))(5 + 2x)(1 + 2x) = 45

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2)(5 + 2x)(1 + 2x) = 45

Multiply (2 + 3x + x2) * (5 + 2x)
(2(5 + 2x) + 3x * (5 + 2x) + x2(5 + 2x))(1 + 2x) = 45
((5 * 2 + 2x * 2) + 3x * (5 + 2x) + x2(5 + 2x))(1 + 2x) = 45
((10 + 4x) + 3x * (5 + 2x) + x2(5 + 2x))(1 + 2x) = 45
(10 + 4x + (5 * 3x + 2x * 3x) + x2(5 + 2x))(1 + 2x) = 45
(10 + 4x + (15x + 6x2) + x2(5 + 2x))(1 + 2x) = 45
(10 + 4x + 15x + 6x2 + (5 * x2 + 2x * x2))(1 + 2x) = 45
(10 + 4x + 15x + 6x2 + (5x2 + 2x3))(1 + 2x) = 45

Combine like terms: 4x + 15x = 19x
(10 + 19x + 6x2 + 5x2 + 2x3)(1 + 2x) = 45

Combine like terms: 6x2 + 5x2 = 11x2
(10 + 19x + 11x2 + 2x3)(1 + 2x) = 45

Multiply (10 + 19x + 11x2 + 2x3) * (1 + 2x)
(10(1 + 2x) + 19x * (1 + 2x) + 11x2 * (1 + 2x) + 2x3 * (1 + 2x)) = 45
((1 * 10 + 2x * 10) + 19x * (1 + 2x) + 11x2 * (1 + 2x) + 2x3 * (1 + 2x)) = 45
((10 + 20x) + 19x * (1 + 2x) + 11x2 * (1 + 2x) + 2x3 * (1 + 2x)) = 45
(10 + 20x + (1 * 19x + 2x * 19x) + 11x2 * (1 + 2x) + 2x3 * (1 + 2x)) = 45
(10 + 20x + (19x + 38x2) + 11x2 * (1 + 2x) + 2x3 * (1 + 2x)) = 45
(10 + 20x + 19x + 38x2 + (1 * 11x2 + 2x * 11x2) + 2x3 * (1 + 2x)) = 45
(10 + 20x + 19x + 38x2 + (11x2 + 22x3) + 2x3 * (1 + 2x)) = 45
(10 + 20x + 19x + 38x2 + 11x2 + 22x3 + (1 * 2x3 + 2x * 2x3)) = 45
(10 + 20x + 19x + 38x2 + 11x2 + 22x3 + (2x3 + 4x4)) = 45

Combine like terms: 20x + 19x = 39x
(10 + 39x + 38x2 + 11x2 + 22x3 + 2x3 + 4x4) = 45

Combine like terms: 38x2 + 11x2 = 49x2
(10 + 39x + 49x2 + 22x3 + 2x3 + 4x4) = 45

Combine like terms: 22x3 + 2x3 = 24x3
(10 + 39x + 49x2 + 24x3 + 4x4) = 45

Solving
10 + 39x + 49x2 + 24x3 + 4x4 = 45

Solving for variable 'x'.

Reorder the terms:
10 + -45 + 39x + 49x2 + 24x3 + 4x4 = 45 + -45

Combine like terms: 10 + -45 = -35
-35 + 39x + 49x2 + 24x3 + 4x4 = 45 + -45

Combine like terms: 45 + -45 = 0
-35 + 39x + 49x2 + 24x3 + 4x4 = 0

The solution to this equation could not be determined.

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