(2x-1)(2x-1)-(3x+2)(3x+2)+5(x-3)(x+3)=1

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Solution for (2x-1)(2x-1)-(3x+2)(3x+2)+5(x-3)(x+3)=1 equation: 


Simplifying
(2x + -1)(2x + -1) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1

Reorder the terms:
(-1 + 2x)(2x + -1) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1

Reorder the terms:
(-1 + 2x)(-1 + 2x) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1
((1 + -2x) + 2x * (-1 + 2x)) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1
(1 + -2x + (-1 * 2x + 2x * 2x)) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1
(1 + -2x + (-2x + 4x2)) + -1(3x + 2)(3x + 2) + 5(x + -3)(x + 3) = 1

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

Reorder the terms:
1 + -4x + 4x2 + -1(2 + 3x)(3x + 2) + 5(x + -3)(x + 3) = 1

Reorder the terms:
1 + -4x + 4x2 + -1(2 + 3x)(2 + 3x) + 5(x + -3)(x + 3) = 1

Multiply (2 + 3x) * (2 + 3x)
1 + -4x + 4x2 + -1(2(2 + 3x) + 3x * (2 + 3x)) + 5(x + -3)(x + 3) = 1
1 + -4x + 4x2 + -1((2 * 2 + 3x * 2) + 3x * (2 + 3x)) + 5(x + -3)(x + 3) = 1
1 + -4x + 4x2 + -1((4 + 6x) + 3x * (2 + 3x)) + 5(x + -3)(x + 3) = 1
1 + -4x + 4x2 + -1(4 + 6x + (2 * 3x + 3x * 3x)) + 5(x + -3)(x + 3) = 1
1 + -4x + 4x2 + -1(4 + 6x + (6x + 9x2)) + 5(x + -3)(x + 3) = 1

Combine like terms: 6x + 6x = 12x
1 + -4x + 4x2 + -1(4 + 12x + 9x2) + 5(x + -3)(x + 3) = 1
1 + -4x + 4x2 + (4 * -1 + 12x * -1 + 9x2 * -1) + 5(x + -3)(x + 3) = 1
1 + -4x + 4x2 + (-4 + -12x + -9x2) + 5(x + -3)(x + 3) = 1

Reorder the terms:
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5(-3 + x)(x + 3) = 1

Reorder the terms:
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5(-3 + x)(3 + x) = 1

Multiply (-3 + x) * (3 + x)
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5(-3(3 + x) + x(3 + x)) = 1
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5((3 * -3 + x * -3) + x(3 + x)) = 1
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5((-9 + -3x) + x(3 + x)) = 1
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5(-9 + -3x + (3 * x + x * x)) = 1
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5(-9 + -3x + (3x + x2)) = 1

Combine like terms: -3x + 3x = 0
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5(-9 + 0 + x2) = 1
1 + -4x + 4x2 + -4 + -12x + -9x2 + 5(-9 + x2) = 1
1 + -4x + 4x2 + -4 + -12x + -9x2 + (-9 * 5 + x2 * 5) = 1
1 + -4x + 4x2 + -4 + -12x + -9x2 + (-45 + 5x2) = 1

Reorder the terms:
1 + -4 + -45 + -4x + -12x + 4x2 + -9x2 + 5x2 = 1

Combine like terms: 1 + -4 = -3
-3 + -45 + -4x + -12x + 4x2 + -9x2 + 5x2 = 1

Combine like terms: -3 + -45 = -48
-48 + -4x + -12x + 4x2 + -9x2 + 5x2 = 1

Combine like terms: -4x + -12x = -16x
-48 + -16x + 4x2 + -9x2 + 5x2 = 1

Combine like terms: 4x2 + -9x2 = -5x2
-48 + -16x + -5x2 + 5x2 = 1

Combine like terms: -5x2 + 5x2 = 0
-48 + -16x + 0 = 1
-48 + -16x = 1

Solving
-48 + -16x = 1

Solving for variable 'x'.

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

Add '48' to each side of the equation.
-48 + 48 + -16x = 1 + 48

Combine like terms: -48 + 48 = 0
0 + -16x = 1 + 48
-16x = 1 + 48

Combine like terms: 1 + 48 = 49
-16x = 49

Divide each side by '-16'.
x = -3.0625

Simplifying
x = -3.0625

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