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

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


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

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

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

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

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

Add '-3' to each side of the equation.
3 + -14x + -3 + 8x2 = 3 + -3

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

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

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

Solving
-14x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-7 + 4x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-7 + 4x)' equal to zero and attempt to solve:

Simplifying
-7 + 4x = 0

Solving
-7 + 4x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4x = 0 + 7
4x = 0 + 7

Combine like terms: 0 + 7 = 7
4x = 7

Divide each side by '4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {0, 1.75}

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