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

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


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

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

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

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

Combine like terms: -8x + -1x = -9x
(2 + -9x + 4x2) = (4x + -1)(2x + -3)

Reorder the terms:
2 + -9x + 4x2 = (-1 + 4x)(2x + -3)

Reorder the terms:
2 + -9x + 4x2 = (-1 + 4x)(-3 + 2x)

Multiply (-1 + 4x) * (-3 + 2x)
2 + -9x + 4x2 = (-1(-3 + 2x) + 4x * (-3 + 2x))
2 + -9x + 4x2 = ((-3 * -1 + 2x * -1) + 4x * (-3 + 2x))
2 + -9x + 4x2 = ((3 + -2x) + 4x * (-3 + 2x))
2 + -9x + 4x2 = (3 + -2x + (-3 * 4x + 2x * 4x))
2 + -9x + 4x2 = (3 + -2x + (-12x + 8x2))

Combine like terms: -2x + -12x = -14x
2 + -9x + 4x2 = (3 + -14x + 8x2)

Solving
2 + -9x + 4x2 = 3 + -14x + 8x2

Solving for variable 'x'.

Reorder the terms:
2 + -3 + -9x + 14x + 4x2 + -8x2 = 3 + -14x + 8x2 + -3 + 14x + -8x2

Combine like terms: 2 + -3 = -1
-1 + -9x + 14x + 4x2 + -8x2 = 3 + -14x + 8x2 + -3 + 14x + -8x2

Combine like terms: -9x + 14x = 5x
-1 + 5x + 4x2 + -8x2 = 3 + -14x + 8x2 + -3 + 14x + -8x2

Combine like terms: 4x2 + -8x2 = -4x2
-1 + 5x + -4x2 = 3 + -14x + 8x2 + -3 + 14x + -8x2

Reorder the terms:
-1 + 5x + -4x2 = 3 + -3 + -14x + 14x + 8x2 + -8x2

Combine like terms: 3 + -3 = 0
-1 + 5x + -4x2 = 0 + -14x + 14x + 8x2 + -8x2
-1 + 5x + -4x2 = -14x + 14x + 8x2 + -8x2

Combine like terms: -14x + 14x = 0
-1 + 5x + -4x2 = 0 + 8x2 + -8x2
-1 + 5x + -4x2 = 8x2 + -8x2

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

Factor a trinomial.
(-1 + x)(1 + -4x) = 0


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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {1, 0.25}

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