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

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


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

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

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

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) + -1(4x + -1)(4x + -1) = 0
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + -1(4x + -1)(4x + -1) = 0
((9 + -6x) + 2x * (-3 + 2x)) + -1(4x + -1)(4x + -1) = 0
(9 + -6x + (-3 * 2x + 2x * 2x)) + -1(4x + -1)(4x + -1) = 0
(9 + -6x + (-6x + 4x2)) + -1(4x + -1)(4x + -1) = 0

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) + -1(4x + -1)(4x + -1) = 0

Reorder the terms:
9 + -12x + 4x2 + -1(-1 + 4x)(4x + -1) = 0

Reorder the terms:
9 + -12x + 4x2 + -1(-1 + 4x)(-1 + 4x) = 0

Multiply (-1 + 4x) * (-1 + 4x)
9 + -12x + 4x2 + -1(-1(-1 + 4x) + 4x * (-1 + 4x)) = 0
9 + -12x + 4x2 + -1((-1 * -1 + 4x * -1) + 4x * (-1 + 4x)) = 0
9 + -12x + 4x2 + -1((1 + -4x) + 4x * (-1 + 4x)) = 0
9 + -12x + 4x2 + -1(1 + -4x + (-1 * 4x + 4x * 4x)) = 0
9 + -12x + 4x2 + -1(1 + -4x + (-4x + 16x2)) = 0

Combine like terms: -4x + -4x = -8x
9 + -12x + 4x2 + -1(1 + -8x + 16x2) = 0
9 + -12x + 4x2 + (1 * -1 + -8x * -1 + 16x2 * -1) = 0
9 + -12x + 4x2 + (-1 + 8x + -16x2) = 0

Reorder the terms:
9 + -1 + -12x + 8x + 4x2 + -16x2 = 0

Combine like terms: 9 + -1 = 8
8 + -12x + 8x + 4x2 + -16x2 = 0

Combine like terms: -12x + 8x = -4x
8 + -4x + 4x2 + -16x2 = 0

Combine like terms: 4x2 + -16x2 = -12x2
8 + -4x + -12x2 = 0

Solving
8 + -4x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -1x + -3x2) = 0

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

Ignore the factor 4.

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 + 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
Solution
x = {0.6666666667, -1}

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