(1-2x)(1-3x)=(6x-1)*x-1

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


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

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

Combine like terms: -3x + -2x = -5x
(1 + -5x + 6x2) = (6x + -1) * x + -1

Reorder the terms:
1 + -5x + 6x2 = (-1 + 6x) * x + -1

Reorder the terms for easier multiplication:
1 + -5x + 6x2 = x(-1 + 6x) + -1
1 + -5x + 6x2 = (-1 * x + 6x * x) + -1
1 + -5x + 6x2 = (-1x + 6x2) + -1

Reorder the terms:
1 + -5x + 6x2 = -1 + -1x + 6x2

Add '-6x2' to each side of the equation.
1 + -5x + 6x2 + -6x2 = -1 + -1x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1 + -5x + 0 = -1 + -1x + 6x2 + -6x2
1 + -5x = -1 + -1x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1 + -5x = -1 + -1x + 0
1 + -5x = -1 + -1x

Solving
1 + -5x = -1 + -1x

Solving for variable 'x'.

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

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

Combine like terms: -5x + x = -4x
1 + -4x = -1 + -1x + x

Combine like terms: -1x + x = 0
1 + -4x = -1 + 0
1 + -4x = -1

Add '-1' to each side of the equation.
1 + -1 + -4x = -1 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = -1 + -1
-4x = -1 + -1

Combine like terms: -1 + -1 = -2
-4x = -2

Divide each side by '-4'.
x = 0.5

Simplifying
x = 0.5

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