(3x-2)(5x+1)=5(2x+7)

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Solution for (3x-2)(5x+1)=5(2x+7) equation: 


Simplifying
(3x + -2)(5x + 1) = 5(2x + 7)

Reorder the terms:
(-2 + 3x)(5x + 1) = 5(2x + 7)

Reorder the terms:
(-2 + 3x)(1 + 5x) = 5(2x + 7)

Multiply (-2 + 3x) * (1 + 5x)
(-2(1 + 5x) + 3x * (1 + 5x)) = 5(2x + 7)
((1 * -2 + 5x * -2) + 3x * (1 + 5x)) = 5(2x + 7)
((-2 + -10x) + 3x * (1 + 5x)) = 5(2x + 7)
(-2 + -10x + (1 * 3x + 5x * 3x)) = 5(2x + 7)
(-2 + -10x + (3x + 15x2)) = 5(2x + 7)

Combine like terms: -10x + 3x = -7x
(-2 + -7x + 15x2) = 5(2x + 7)

Reorder the terms:
-2 + -7x + 15x2 = 5(7 + 2x)
-2 + -7x + 15x2 = (7 * 5 + 2x * 5)
-2 + -7x + 15x2 = (35 + 10x)

Solving
-2 + -7x + 15x2 = 35 + 10x

Solving for variable 'x'.

Reorder the terms:
-2 + -35 + -7x + -10x + 15x2 = 35 + 10x + -35 + -10x

Combine like terms: -2 + -35 = -37
-37 + -7x + -10x + 15x2 = 35 + 10x + -35 + -10x

Combine like terms: -7x + -10x = -17x
-37 + -17x + 15x2 = 35 + 10x + -35 + -10x

Reorder the terms:
-37 + -17x + 15x2 = 35 + -35 + 10x + -10x

Combine like terms: 35 + -35 = 0
-37 + -17x + 15x2 = 0 + 10x + -10x
-37 + -17x + 15x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-37 + -17x + 15x2 = 0

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

Divide each side by '15'.
-2.466666667 + -1.133333333x + x2 = 0

Move the constant term to the right:

Add '2.466666667' to each side of the equation.
-2.466666667 + -1.133333333x + 2.466666667 + x2 = 0 + 2.466666667

Reorder the terms:
-2.466666667 + 2.466666667 + -1.133333333x + x2 = 0 + 2.466666667

Combine like terms: -2.466666667 + 2.466666667 = 0.000000000
0.000000000 + -1.133333333x + x2 = 0 + 2.466666667
-1.133333333x + x2 = 0 + 2.466666667

Combine like terms: 0 + 2.466666667 = 2.466666667
-1.133333333x + x2 = 2.466666667

The x term is -1.133333333x.  Take half its coefficient (-0.5666666665).
Square it (0.3211111109) and add it to both sides.

Add '0.3211111109' to each side of the equation.
-1.133333333x + 0.3211111109 + x2 = 2.466666667 + 0.3211111109

Reorder the terms:
0.3211111109 + -1.133333333x + x2 = 2.466666667 + 0.3211111109

Combine like terms: 2.466666667 + 0.3211111109 = 2.7877777779
0.3211111109 + -1.133333333x + x2 = 2.7877777779

Factor a perfect square on the left side:
(x + -0.5666666665)(x + -0.5666666665) = 2.7877777779

Calculate the square root of the right side: 1.669663972

Break this problem into two subproblems by setting 
(x + -0.5666666665) equal to 1.669663972 and -1.669663972.


Subproblem 1
x + -0.5666666665 = 1.669663972

Simplifying
x + -0.5666666665 = 1.669663972

Reorder the terms:
-0.5666666665 + x = 1.669663972

Solving
-0.5666666665 + x = 1.669663972

Solving for variable 'x'.

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

Add '0.5666666665' to each side of the equation.
-0.5666666665 + 0.5666666665 + x = 1.669663972 + 0.5666666665

Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000
0.0000000000 + x = 1.669663972 + 0.5666666665
x = 1.669663972 + 0.5666666665

Combine like terms: 1.669663972 + 0.5666666665 = 2.2363306385
x = 2.2363306385

Simplifying
x = 2.2363306385


Subproblem 2
x + -0.5666666665 = -1.669663972

Simplifying
x + -0.5666666665 = -1.669663972

Reorder the terms:
-0.5666666665 + x = -1.669663972

Solving
-0.5666666665 + x = -1.669663972

Solving for variable 'x'.

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

Add '0.5666666665' to each side of the equation.
-0.5666666665 + 0.5666666665 + x = -1.669663972 + 0.5666666665

Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000
0.0000000000 + x = -1.669663972 + 0.5666666665
x = -1.669663972 + 0.5666666665

Combine like terms: -1.669663972 + 0.5666666665 = -1.1029973055
x = -1.1029973055

Simplifying
x = -1.1029973055


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2363306385, -1.1029973055}

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