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

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


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

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

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

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

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

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

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

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

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

Solving
-2 + 2x + 4x2 = 1 + -5x + 6x2

Solving for variable 'x'.

Reorder the terms:
-2 + -1 + 2x + 5x + 4x2 + -6x2 = 1 + -5x + 6x2 + -1 + 5x + -6x2

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

Combine like terms: 2x + 5x = 7x
-3 + 7x + 4x2 + -6x2 = 1 + -5x + 6x2 + -1 + 5x + -6x2

Combine like terms: 4x2 + -6x2 = -2x2
-3 + 7x + -2x2 = 1 + -5x + 6x2 + -1 + 5x + -6x2

Reorder the terms:
-3 + 7x + -2x2 = 1 + -1 + -5x + 5x + 6x2 + -6x2

Combine like terms: 1 + -1 = 0
-3 + 7x + -2x2 = 0 + -5x + 5x + 6x2 + -6x2
-3 + 7x + -2x2 = -5x + 5x + 6x2 + -6x2

Combine like terms: -5x + 5x = 0
-3 + 7x + -2x2 = 0 + 6x2 + -6x2
-3 + 7x + -2x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-3 + 7x + -2x2 = 0

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


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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

Simplifying
x = 3

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 = {3, 0.5}

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