2(x-4)(3x+5)=7x+(6x-5)

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Solution for 2(x-4)(3x+5)=7x+(6x-5) equation: 


Simplifying
2(x + -4)(3x + 5) = 7x + (6x + -5)

Reorder the terms:
2(-4 + x)(3x + 5) = 7x + (6x + -5)

Reorder the terms:
2(-4 + x)(5 + 3x) = 7x + (6x + -5)

Multiply (-4 + x) * (5 + 3x)
2(-4(5 + 3x) + x(5 + 3x)) = 7x + (6x + -5)
2((5 * -4 + 3x * -4) + x(5 + 3x)) = 7x + (6x + -5)
2((-20 + -12x) + x(5 + 3x)) = 7x + (6x + -5)
2(-20 + -12x + (5 * x + 3x * x)) = 7x + (6x + -5)
2(-20 + -12x + (5x + 3x2)) = 7x + (6x + -5)

Combine like terms: -12x + 5x = -7x
2(-20 + -7x + 3x2) = 7x + (6x + -5)
(-20 * 2 + -7x * 2 + 3x2 * 2) = 7x + (6x + -5)
(-40 + -14x + 6x2) = 7x + (6x + -5)

Reorder the terms:
-40 + -14x + 6x2 = 7x + (-5 + 6x)

Remove parenthesis around (-5 + 6x)
-40 + -14x + 6x2 = 7x + -5 + 6x

Reorder the terms:
-40 + -14x + 6x2 = -5 + 7x + 6x

Combine like terms: 7x + 6x = 13x
-40 + -14x + 6x2 = -5 + 13x

Solving
-40 + -14x + 6x2 = -5 + 13x

Solving for variable 'x'.

Reorder the terms:
-40 + 5 + -14x + -13x + 6x2 = -5 + 13x + 5 + -13x

Combine like terms: -40 + 5 = -35
-35 + -14x + -13x + 6x2 = -5 + 13x + 5 + -13x

Combine like terms: -14x + -13x = -27x
-35 + -27x + 6x2 = -5 + 13x + 5 + -13x

Reorder the terms:
-35 + -27x + 6x2 = -5 + 5 + 13x + -13x

Combine like terms: -5 + 5 = 0
-35 + -27x + 6x2 = 0 + 13x + -13x
-35 + -27x + 6x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-35 + -27x + 6x2 = 0

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

Divide each side by '6'.
-5.833333333 + -4.5x + x2 = 0

Move the constant term to the right:

Add '5.833333333' to each side of the equation.
-5.833333333 + -4.5x + 5.833333333 + x2 = 0 + 5.833333333

Reorder the terms:
-5.833333333 + 5.833333333 + -4.5x + x2 = 0 + 5.833333333

Combine like terms: -5.833333333 + 5.833333333 = 0.000000000
0.000000000 + -4.5x + x2 = 0 + 5.833333333
-4.5x + x2 = 0 + 5.833333333

Combine like terms: 0 + 5.833333333 = 5.833333333
-4.5x + x2 = 5.833333333

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 5.833333333 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 5.833333333 + 5.0625

Combine like terms: 5.833333333 + 5.0625 = 10.895833333
5.0625 + -4.5x + x2 = 10.895833333

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 10.895833333

Calculate the square root of the right side: 3.30088372

Break this problem into two subproblems by setting 
(x + -2.25) equal to 3.30088372 and -3.30088372.


Subproblem 1
x + -2.25 = 3.30088372

Simplifying
x + -2.25 = 3.30088372

Reorder the terms:
-2.25 + x = 3.30088372

Solving
-2.25 + x = 3.30088372

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 3.30088372 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 3.30088372 + 2.25
x = 3.30088372 + 2.25

Combine like terms: 3.30088372 + 2.25 = 5.55088372
x = 5.55088372

Simplifying
x = 5.55088372


Subproblem 2
x + -2.25 = -3.30088372

Simplifying
x + -2.25 = -3.30088372

Reorder the terms:
-2.25 + x = -3.30088372

Solving
-2.25 + x = -3.30088372

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -3.30088372 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -3.30088372 + 2.25
x = -3.30088372 + 2.25

Combine like terms: -3.30088372 + 2.25 = -1.05088372
x = -1.05088372

Simplifying
x = -1.05088372


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.55088372, -1.05088372}

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