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

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


Simplifying
(2x + -1)(4 + -3x) + (1 + -2x) = 0

Reorder the terms:
(-1 + 2x)(4 + -3x) + (1 + -2x) = 0

Multiply (-1 + 2x) * (4 + -3x)
(-1(4 + -3x) + 2x * (4 + -3x)) + (1 + -2x) = 0
((4 * -1 + -3x * -1) + 2x * (4 + -3x)) + (1 + -2x) = 0
((-4 + 3x) + 2x * (4 + -3x)) + (1 + -2x) = 0
(-4 + 3x + (4 * 2x + -3x * 2x)) + (1 + -2x) = 0
(-4 + 3x + (8x + -6x2)) + (1 + -2x) = 0

Combine like terms: 3x + 8x = 11x
(-4 + 11x + -6x2) + (1 + -2x) = 0

Remove parenthesis around (1 + -2x)
-4 + 11x + -6x2 + 1 + -2x = 0

Reorder the terms:
-4 + 1 + 11x + -2x + -6x2 = 0

Combine like terms: -4 + 1 = -3
-3 + 11x + -2x + -6x2 = 0

Combine like terms: 11x + -2x = 9x
-3 + 9x + -6x2 = 0

Solving
-3 + 9x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 3x + -2x2) = 0

Factor a trinomial.
3((-1 + x)(1 + -2x)) = 0

Ignore the factor 3.

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

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {1, 0.5}

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