(3x+12)(4x-8)=x

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Solution for (3x+12)(4x-8)=x equation:


Simplifying
(3x + 12)(4x + -8) = x

Reorder the terms:
(12 + 3x)(4x + -8) = x

Reorder the terms:
(12 + 3x)(-8 + 4x) = x

Multiply (12 + 3x) * (-8 + 4x)
(12(-8 + 4x) + 3x * (-8 + 4x)) = x
((-8 * 12 + 4x * 12) + 3x * (-8 + 4x)) = x
((-96 + 48x) + 3x * (-8 + 4x)) = x
(-96 + 48x + (-8 * 3x + 4x * 3x)) = x
(-96 + 48x + (-24x + 12x2)) = x

Combine like terms: 48x + -24x = 24x
(-96 + 24x + 12x2) = x

Solving
-96 + 24x + 12x2 = x

Solving for variable 'x'.

Reorder the terms:
-96 + 24x + -1x + 12x2 = x + -1x

Combine like terms: 24x + -1x = 23x
-96 + 23x + 12x2 = x + -1x

Combine like terms: x + -1x = 0
-96 + 23x + 12x2 = 0

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

Divide each side by '12'.
-8 + 1.916666667x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1.916666667x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 1.916666667x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1.916666667x + x2 = 0 + 8
1.916666667x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
1.916666667x + x2 = 8

The x term is 1.916666667x.  Take half its coefficient (0.9583333335).
Square it (0.9184027781) and add it to both sides.

Add '0.9184027781' to each side of the equation.
1.916666667x + 0.9184027781 + x2 = 8 + 0.9184027781

Reorder the terms:
0.9184027781 + 1.916666667x + x2 = 8 + 0.9184027781

Combine like terms: 8 + 0.9184027781 = 8.9184027781
0.9184027781 + 1.916666667x + x2 = 8.9184027781

Factor a perfect square on the left side:
(x + 0.9583333335)(x + 0.9583333335) = 8.9184027781

Calculate the square root of the right side: 2.986369498

Break this problem into two subproblems by setting 
(x + 0.9583333335) equal to 2.986369498 and -2.986369498.

Subproblem 1

x + 0.9583333335 = 2.986369498 Simplifying x + 0.9583333335 = 2.986369498 Reorder the terms: 0.9583333335 + x = 2.986369498 Solving 0.9583333335 + x = 2.986369498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = 2.986369498 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = 2.986369498 + -0.9583333335 x = 2.986369498 + -0.9583333335 Combine like terms: 2.986369498 + -0.9583333335 = 2.0280361645 x = 2.0280361645 Simplifying x = 2.0280361645

Subproblem 2

x + 0.9583333335 = -2.986369498 Simplifying x + 0.9583333335 = -2.986369498 Reorder the terms: 0.9583333335 + x = -2.986369498 Solving 0.9583333335 + x = -2.986369498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = -2.986369498 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = -2.986369498 + -0.9583333335 x = -2.986369498 + -0.9583333335 Combine like terms: -2.986369498 + -0.9583333335 = -3.9447028315 x = -3.9447028315 Simplifying x = -3.9447028315

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.0280361645, -3.9447028315}

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