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

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


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

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

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

Combine like terms: 6x + -1x = 5x
(3 + 5x + -2x2) + -1(2x + 1)(1 + -4x) = 0

Reorder the terms:
3 + 5x + -2x2 + -1(1 + 2x)(1 + -4x) = 0

Multiply (1 + 2x) * (1 + -4x)
3 + 5x + -2x2 + -1(1(1 + -4x) + 2x * (1 + -4x)) = 0
3 + 5x + -2x2 + -1((1 * 1 + -4x * 1) + 2x * (1 + -4x)) = 0
3 + 5x + -2x2 + -1((1 + -4x) + 2x * (1 + -4x)) = 0
3 + 5x + -2x2 + -1(1 + -4x + (1 * 2x + -4x * 2x)) = 0
3 + 5x + -2x2 + -1(1 + -4x + (2x + -8x2)) = 0

Combine like terms: -4x + 2x = -2x
3 + 5x + -2x2 + -1(1 + -2x + -8x2) = 0
3 + 5x + -2x2 + (1 * -1 + -2x * -1 + -8x2 * -1) = 0
3 + 5x + -2x2 + (-1 + 2x + 8x2) = 0

Reorder the terms:
3 + -1 + 5x + 2x + -2x2 + 8x2 = 0

Combine like terms: 3 + -1 = 2
2 + 5x + 2x + -2x2 + 8x2 = 0

Combine like terms: 5x + 2x = 7x
2 + 7x + -2x2 + 8x2 = 0

Combine like terms: -2x2 + 8x2 = 6x2
2 + 7x + 6x2 = 0

Solving
2 + 7x + 6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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 = {-0.6666666667, -0.5}

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