(2x-1)(4x-3)=6

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Solution for (2x-1)(4x-3)=6 equation: 


Simplifying
(2x + -1)(4x + -3) = 6

Reorder the terms:
(-1 + 2x)(4x + -3) = 6

Reorder the terms:
(-1 + 2x)(-3 + 4x) = 6

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

Combine like terms: -4x + -6x = -10x
(3 + -10x + 8x2) = 6

Solving
3 + -10x + 8x2 = 6

Solving for variable 'x'.

Reorder the terms:
3 + -6 + -10x + 8x2 = 6 + -6

Combine like terms: 3 + -6 = -3
-3 + -10x + 8x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-3 + -10x + 8x2 = 0

Factor a trinomial.
(-1 + -4x)(3 + -2x) = 0


Subproblem 1
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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.25, 1.5}

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