(1-2x)(3+5x)=(1-x)(x+1+3-6x)

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Solution for (1-2x)(3+5x)=(1-x)(x+1+3-6x) equation: 


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

Multiply (1 + -2x) * (3 + 5x)
(1(3 + 5x) + -2x * (3 + 5x)) = (1 + -1x)(x + 1 + 3 + -6x)
((3 * 1 + 5x * 1) + -2x * (3 + 5x)) = (1 + -1x)(x + 1 + 3 + -6x)
((3 + 5x) + -2x * (3 + 5x)) = (1 + -1x)(x + 1 + 3 + -6x)
(3 + 5x + (3 * -2x + 5x * -2x)) = (1 + -1x)(x + 1 + 3 + -6x)
(3 + 5x + (-6x + -10x2)) = (1 + -1x)(x + 1 + 3 + -6x)

Combine like terms: 5x + -6x = -1x
(3 + -1x + -10x2) = (1 + -1x)(x + 1 + 3 + -6x)

Reorder the terms:
3 + -1x + -10x2 = (1 + -1x)(1 + 3 + x + -6x)

Combine like terms: 1 + 3 = 4
3 + -1x + -10x2 = (1 + -1x)(4 + x + -6x)

Combine like terms: x + -6x = -5x
3 + -1x + -10x2 = (1 + -1x)(4 + -5x)

Multiply (1 + -1x) * (4 + -5x)
3 + -1x + -10x2 = (1(4 + -5x) + -1x * (4 + -5x))
3 + -1x + -10x2 = ((4 * 1 + -5x * 1) + -1x * (4 + -5x))
3 + -1x + -10x2 = ((4 + -5x) + -1x * (4 + -5x))
3 + -1x + -10x2 = (4 + -5x + (4 * -1x + -5x * -1x))
3 + -1x + -10x2 = (4 + -5x + (-4x + 5x2))

Combine like terms: -5x + -4x = -9x
3 + -1x + -10x2 = (4 + -9x + 5x2)

Solving
3 + -1x + -10x2 = 4 + -9x + 5x2

Solving for variable 'x'.

Reorder the terms:
3 + -4 + -1x + 9x + -10x2 + -5x2 = 4 + -9x + 5x2 + -4 + 9x + -5x2

Combine like terms: 3 + -4 = -1
-1 + -1x + 9x + -10x2 + -5x2 = 4 + -9x + 5x2 + -4 + 9x + -5x2

Combine like terms: -1x + 9x = 8x
-1 + 8x + -10x2 + -5x2 = 4 + -9x + 5x2 + -4 + 9x + -5x2

Combine like terms: -10x2 + -5x2 = -15x2
-1 + 8x + -15x2 = 4 + -9x + 5x2 + -4 + 9x + -5x2

Reorder the terms:
-1 + 8x + -15x2 = 4 + -4 + -9x + 9x + 5x2 + -5x2

Combine like terms: 4 + -4 = 0
-1 + 8x + -15x2 = 0 + -9x + 9x + 5x2 + -5x2
-1 + 8x + -15x2 = -9x + 9x + 5x2 + -5x2

Combine like terms: -9x + 9x = 0
-1 + 8x + -15x2 = 0 + 5x2 + -5x2
-1 + 8x + -15x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1 + 8x + -15x2 = 0

Factor a trinomial.
(-1 + 3x)(1 + -5x) = 0


Subproblem 1
Set the factor '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3x = 0 + 1

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

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

Divide each side by '3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {0.3333333333, 0.2}

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