-6(3x-1)(3x+1)-5(2x+1)(x-4)=3

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Solution for -6(3x-1)(3x+1)-5(2x+1)(x-4)=3 equation:


Simplifying
-6(3x + -1)(3x + 1) + -5(2x + 1)(x + -4) = 3

Reorder the terms:
-6(-1 + 3x)(3x + 1) + -5(2x + 1)(x + -4) = 3

Reorder the terms:
-6(-1 + 3x)(1 + 3x) + -5(2x + 1)(x + -4) = 3

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

Combine like terms: -3x + 3x = 0
-6(-1 + 0 + 9x2) + -5(2x + 1)(x + -4) = 3
-6(-1 + 9x2) + -5(2x + 1)(x + -4) = 3
(-1 * -6 + 9x2 * -6) + -5(2x + 1)(x + -4) = 3
(6 + -54x2) + -5(2x + 1)(x + -4) = 3

Reorder the terms:
6 + -54x2 + -5(1 + 2x)(x + -4) = 3

Reorder the terms:
6 + -54x2 + -5(1 + 2x)(-4 + x) = 3

Multiply (1 + 2x) * (-4 + x)
6 + -54x2 + -5(1(-4 + x) + 2x * (-4 + x)) = 3
6 + -54x2 + -5((-4 * 1 + x * 1) + 2x * (-4 + x)) = 3
6 + -54x2 + -5((-4 + 1x) + 2x * (-4 + x)) = 3
6 + -54x2 + -5(-4 + 1x + (-4 * 2x + x * 2x)) = 3
6 + -54x2 + -5(-4 + 1x + (-8x + 2x2)) = 3

Combine like terms: 1x + -8x = -7x
6 + -54x2 + -5(-4 + -7x + 2x2) = 3
6 + -54x2 + (-4 * -5 + -7x * -5 + 2x2 * -5) = 3
6 + -54x2 + (20 + 35x + -10x2) = 3

Reorder the terms:
6 + 20 + 35x + -54x2 + -10x2 = 3

Combine like terms: 6 + 20 = 26
26 + 35x + -54x2 + -10x2 = 3

Combine like terms: -54x2 + -10x2 = -64x2
26 + 35x + -64x2 = 3

Solving
26 + 35x + -64x2 = 3

Solving for variable 'x'.

Reorder the terms:
26 + -3 + 35x + -64x2 = 3 + -3

Combine like terms: 26 + -3 = 23
23 + 35x + -64x2 = 3 + -3

Combine like terms: 3 + -3 = 0
23 + 35x + -64x2 = 0

Begin completing the square.  Divide all terms by
-64 the coefficient of the squared term: 

Divide each side by '-64'.
-0.359375 + -0.546875x + x2 = 0

Move the constant term to the right:

Add '0.359375' to each side of the equation.
-0.359375 + -0.546875x + 0.359375 + x2 = 0 + 0.359375

Reorder the terms:
-0.359375 + 0.359375 + -0.546875x + x2 = 0 + 0.359375

Combine like terms: -0.359375 + 0.359375 = 0.000000
0.000000 + -0.546875x + x2 = 0 + 0.359375
-0.546875x + x2 = 0 + 0.359375

Combine like terms: 0 + 0.359375 = 0.359375
-0.546875x + x2 = 0.359375

The x term is -0.546875x.  Take half its coefficient (-0.2734375).
Square it (0.07476806641) and add it to both sides.

Add '0.07476806641' to each side of the equation.
-0.546875x + 0.07476806641 + x2 = 0.359375 + 0.07476806641

Reorder the terms:
0.07476806641 + -0.546875x + x2 = 0.359375 + 0.07476806641

Combine like terms: 0.359375 + 0.07476806641 = 0.43414306641
0.07476806641 + -0.546875x + x2 = 0.43414306641

Factor a perfect square on the left side:
(x + -0.2734375)(x + -0.2734375) = 0.43414306641

Calculate the square root of the right side: 0.658895338

Break this problem into two subproblems by setting 
(x + -0.2734375) equal to 0.658895338 and -0.658895338.

Subproblem 1

x + -0.2734375 = 0.658895338 Simplifying x + -0.2734375 = 0.658895338 Reorder the terms: -0.2734375 + x = 0.658895338 Solving -0.2734375 + x = 0.658895338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2734375' to each side of the equation. -0.2734375 + 0.2734375 + x = 0.658895338 + 0.2734375 Combine like terms: -0.2734375 + 0.2734375 = 0.0000000 0.0000000 + x = 0.658895338 + 0.2734375 x = 0.658895338 + 0.2734375 Combine like terms: 0.658895338 + 0.2734375 = 0.932332838 x = 0.932332838 Simplifying x = 0.932332838

Subproblem 2

x + -0.2734375 = -0.658895338 Simplifying x + -0.2734375 = -0.658895338 Reorder the terms: -0.2734375 + x = -0.658895338 Solving -0.2734375 + x = -0.658895338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2734375' to each side of the equation. -0.2734375 + 0.2734375 + x = -0.658895338 + 0.2734375 Combine like terms: -0.2734375 + 0.2734375 = 0.0000000 0.0000000 + x = -0.658895338 + 0.2734375 x = -0.658895338 + 0.2734375 Combine like terms: -0.658895338 + 0.2734375 = -0.385457838 x = -0.385457838 Simplifying x = -0.385457838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.932332838, -0.385457838}

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