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

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

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

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

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

Reorder the terms for easier multiplication:
5 * 2(-6 + x)(7 + 3x) = 2(3x + 5)

Multiply 5 * 2
10(-6 + x)(7 + 3x) = 2(3x + 5)

Multiply (-6 + x) * (7 + 3x)
10(-6(7 + 3x) + x(7 + 3x)) = 2(3x + 5)
10((7 * -6 + 3x * -6) + x(7 + 3x)) = 2(3x + 5)
10((-42 + -18x) + x(7 + 3x)) = 2(3x + 5)
10(-42 + -18x + (7 * x + 3x * x)) = 2(3x + 5)
10(-42 + -18x + (7x + 3x2)) = 2(3x + 5)

Combine like terms: -18x + 7x = -11x
10(-42 + -11x + 3x2) = 2(3x + 5)
(-42 * 10 + -11x * 10 + 3x2 * 10) = 2(3x + 5)
(-420 + -110x + 30x2) = 2(3x + 5)

Reorder the terms:
-420 + -110x + 30x2 = 2(5 + 3x)
-420 + -110x + 30x2 = (5 * 2 + 3x * 2)
-420 + -110x + 30x2 = (10 + 6x)

Solving
-420 + -110x + 30x2 = 10 + 6x

Solving for variable 'x'.

Reorder the terms:
-420 + -10 + -110x + -6x + 30x2 = 10 + 6x + -10 + -6x

Combine like terms: -420 + -10 = -430
-430 + -110x + -6x + 30x2 = 10 + 6x + -10 + -6x

Combine like terms: -110x + -6x = -116x
-430 + -116x + 30x2 = 10 + 6x + -10 + -6x

Reorder the terms:
-430 + -116x + 30x2 = 10 + -10 + 6x + -6x

Combine like terms: 10 + -10 = 0
-430 + -116x + 30x2 = 0 + 6x + -6x
-430 + -116x + 30x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-430 + -116x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-215 + -58x + 15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-215 + -58x + 15x2)' equal to zero and attempt to solve:

Simplifying
-215 + -58x + 15x2 = 0

Solving
-215 + -58x + 15x2 = 0

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

Divide each side by '15'.
-14.33333333 + -3.866666667x + x2 = 0

Move the constant term to the right:

Add '14.33333333' to each side of the equation.
-14.33333333 + -3.866666667x + 14.33333333 + x2 = 0 + 14.33333333

Reorder the terms:
-14.33333333 + 14.33333333 + -3.866666667x + x2 = 0 + 14.33333333

Combine like terms: -14.33333333 + 14.33333333 = 0.00000000
0.00000000 + -3.866666667x + x2 = 0 + 14.33333333
-3.866666667x + x2 = 0 + 14.33333333

Combine like terms: 0 + 14.33333333 = 14.33333333
-3.866666667x + x2 = 14.33333333

The x term is -3.866666667x.  Take half its coefficient (-1.933333334).
Square it (3.737777780) and add it to both sides.

Add '3.737777780' to each side of the equation.
-3.866666667x + 3.737777780 + x2 = 14.33333333 + 3.737777780

Reorder the terms:
3.737777780 + -3.866666667x + x2 = 14.33333333 + 3.737777780

Combine like terms: 14.33333333 + 3.737777780 = 18.07111111
3.737777780 + -3.866666667x + x2 = 18.07111111

Factor a perfect square on the left side:
(x + -1.933333334)(x + -1.933333334) = 18.07111111

Calculate the square root of the right side: 4.251012951

Break this problem into two subproblems by setting 
(x + -1.933333334) equal to 4.251012951 and -4.251012951.

Subproblem 1
x + -1.933333334 = 4.251012951

Simplifying
x + -1.933333334 = 4.251012951

Reorder the terms:
-1.933333334 + x = 4.251012951

Solving
-1.933333334 + x = 4.251012951

Solving for variable 'x'.

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

Add '1.933333334' to each side of the equation.
-1.933333334 + 1.933333334 + x = 4.251012951 + 1.933333334

Combine like terms: -1.933333334 + 1.933333334 = 0.000000000
0.000000000 + x = 4.251012951 + 1.933333334
x = 4.251012951 + 1.933333334

Combine like terms: 4.251012951 + 1.933333334 = 6.184346285
x = 6.184346285

Simplifying
x = 6.184346285

Subproblem 2
x + -1.933333334 = -4.251012951

Simplifying
x + -1.933333334 = -4.251012951

Reorder the terms:
-1.933333334 + x = -4.251012951

Solving
-1.933333334 + x = -4.251012951

Solving for variable 'x'.

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

Add '1.933333334' to each side of the equation.
-1.933333334 + 1.933333334 + x = -4.251012951 + 1.933333334

Combine like terms: -1.933333334 + 1.933333334 = 0.000000000
0.000000000 + x = -4.251012951 + 1.933333334
x = -4.251012951 + 1.933333334

Combine like terms: -4.251012951 + 1.933333334 = -2.317679617
x = -2.317679617

Simplifying
x = -2.317679617

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.184346285, -2.317679617}
Solution
x = {6.184346285, -2.317679617}