(1-3x)*(1-4x+x^2)+(3x-1)*(1-5x+x^2)+3x^2=0

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Solution for (1-3x)*(1-4x+x^2)+(3x-1)*(1-5x+x^2)+3x^2=0 equation:


Simplifying
(1 + -3x)(1 + -4x + x2) + (3x + -1)(1 + -5x + x2) + 3x2 = 0

Multiply (1 + -3x) * (1 + -4x + x2)
(1(1 + -4x + x2) + -3x * (1 + -4x + x2)) + (3x + -1)(1 + -5x + x2) + 3x2 = 0
((1 * 1 + -4x * 1 + x2 * 1) + -3x * (1 + -4x + x2)) + (3x + -1)(1 + -5x + x2) + 3x2 = 0
((1 + -4x + 1x2) + -3x * (1 + -4x + x2)) + (3x + -1)(1 + -5x + x2) + 3x2 = 0
(1 + -4x + 1x2 + (1 * -3x + -4x * -3x + x2 * -3x)) + (3x + -1)(1 + -5x + x2) + 3x2 = 0
(1 + -4x + 1x2 + (-3x + 12x2 + -3x3)) + (3x + -1)(1 + -5x + x2) + 3x2 = 0

Reorder the terms:
(1 + -4x + -3x + 1x2 + 12x2 + -3x3) + (3x + -1)(1 + -5x + x2) + 3x2 = 0

Combine like terms: -4x + -3x = -7x
(1 + -7x + 1x2 + 12x2 + -3x3) + (3x + -1)(1 + -5x + x2) + 3x2 = 0

Combine like terms: 1x2 + 12x2 = 13x2
(1 + -7x + 13x2 + -3x3) + (3x + -1)(1 + -5x + x2) + 3x2 = 0

Reorder the terms:
1 + -7x + 13x2 + -3x3 + (-1 + 3x)(1 + -5x + x2) + 3x2 = 0

Multiply (-1 + 3x) * (1 + -5x + x2)
1 + -7x + 13x2 + -3x3 + (-1(1 + -5x + x2) + 3x * (1 + -5x + x2)) + 3x2 = 0
1 + -7x + 13x2 + -3x3 + ((1 * -1 + -5x * -1 + x2 * -1) + 3x * (1 + -5x + x2)) + 3x2 = 0
1 + -7x + 13x2 + -3x3 + ((-1 + 5x + -1x2) + 3x * (1 + -5x + x2)) + 3x2 = 0
1 + -7x + 13x2 + -3x3 + (-1 + 5x + -1x2 + (1 * 3x + -5x * 3x + x2 * 3x)) + 3x2 = 0
1 + -7x + 13x2 + -3x3 + (-1 + 5x + -1x2 + (3x + -15x2 + 3x3)) + 3x2 = 0

Reorder the terms:
1 + -7x + 13x2 + -3x3 + (-1 + 5x + 3x + -1x2 + -15x2 + 3x3) + 3x2 = 0

Combine like terms: 5x + 3x = 8x
1 + -7x + 13x2 + -3x3 + (-1 + 8x + -1x2 + -15x2 + 3x3) + 3x2 = 0

Combine like terms: -1x2 + -15x2 = -16x2
1 + -7x + 13x2 + -3x3 + (-1 + 8x + -16x2 + 3x3) + 3x2 = 0

Reorder the terms:
1 + -1 + -7x + 8x + 13x2 + -16x2 + 3x2 + -3x3 + 3x3 = 0

Combine like terms: 1 + -1 = 0
0 + -7x + 8x + 13x2 + -16x2 + 3x2 + -3x3 + 3x3 = 0
-7x + 8x + 13x2 + -16x2 + 3x2 + -3x3 + 3x3 = 0

Combine like terms: -7x + 8x = 1x
1x + 13x2 + -16x2 + 3x2 + -3x3 + 3x3 = 0

Combine like terms: 13x2 + -16x2 = -3x2
1x + -3x2 + 3x2 + -3x3 + 3x3 = 0

Combine like terms: -3x2 + 3x2 = 0
1x + 0 + -3x3 + 3x3 = 0
1x + -3x3 + 3x3 = 0

Combine like terms: -3x3 + 3x3 = 0
1x + 0 = 0
1x = 0

Solving
1x = 0

Solving for variable 'x'.

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

Divide each side by '1'.
x = 0

Simplifying
x = 0

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