3(2x+1)(-x+3)-(2x+5)(2x+5)=-[-(-3(x+5))+(10x)(10x)]

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Solution for 3(2x+1)(-x+3)-(2x+5)(2x+5)=-[-(-3(x+5))+(10x)(10x)] equation: 


Simplifying
3(2x + 1)(-1x + 3) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]

Reorder the terms:
3(1 + 2x)(-1x + 3) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]

Reorder the terms:
3(1 + 2x)(3 + -1x) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]

Multiply (1 + 2x) * (3 + -1x)
3(1(3 + -1x) + 2x * (3 + -1x)) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]
3((3 * 1 + -1x * 1) + 2x * (3 + -1x)) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]
3((3 + -1x) + 2x * (3 + -1x)) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]
3(3 + -1x + (3 * 2x + -1x * 2x)) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]
3(3 + -1x + (6x + -2x2)) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]

Combine like terms: -1x + 6x = 5x
3(3 + 5x + -2x2) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]
(3 * 3 + 5x * 3 + -2x2 * 3) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]
(9 + 15x + -6x2) + -1(2x + 5)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]

Reorder the terms:
9 + 15x + -6x2 + -1(5 + 2x)(2x + 5) = -1[-1(-3(x + 5)) + (10x)(10x)]

Reorder the terms:
9 + 15x + -6x2 + -1(5 + 2x)(5 + 2x) = -1[-1(-3(x + 5)) + (10x)(10x)]

Multiply (5 + 2x) * (5 + 2x)
9 + 15x + -6x2 + -1(5(5 + 2x) + 2x * (5 + 2x)) = -1[-1(-3(x + 5)) + (10x)(10x)]
9 + 15x + -6x2 + -1((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = -1[-1(-3(x + 5)) + (10x)(10x)]
9 + 15x + -6x2 + -1((25 + 10x) + 2x * (5 + 2x)) = -1[-1(-3(x + 5)) + (10x)(10x)]
9 + 15x + -6x2 + -1(25 + 10x + (5 * 2x + 2x * 2x)) = -1[-1(-3(x + 5)) + (10x)(10x)]
9 + 15x + -6x2 + -1(25 + 10x + (10x + 4x2)) = -1[-1(-3(x + 5)) + (10x)(10x)]

Combine like terms: 10x + 10x = 20x
9 + 15x + -6x2 + -1(25 + 20x + 4x2) = -1[-1(-3(x + 5)) + (10x)(10x)]
9 + 15x + -6x2 + (25 * -1 + 20x * -1 + 4x2 * -1) = -1[-1(-3(x + 5)) + (10x)(10x)]
9 + 15x + -6x2 + (-25 + -20x + -4x2) = -1[-1(-3(x + 5)) + (10x)(10x)]

Reorder the terms:
9 + -25 + 15x + -20x + -6x2 + -4x2 = -1[-1(-3(x + 5)) + (10x)(10x)]

Combine like terms: 9 + -25 = -16
-16 + 15x + -20x + -6x2 + -4x2 = -1[-1(-3(x + 5)) + (10x)(10x)]

Combine like terms: 15x + -20x = -5x
-16 + -5x + -6x2 + -4x2 = -1[-1(-3(x + 5)) + (10x)(10x)]

Combine like terms: -6x2 + -4x2 = -10x2
-16 + -5x + -10x2 = -1[-1(-3(x + 5)) + (10x)(10x)]

Reorder the terms:
-16 + -5x + -10x2 = -1[-1(-3(5 + x)) + (10x)(10x)]
-16 + -5x + -10x2 = -1[-1((5 * -3 + x * -3)) + (10x)(10x)]
-16 + -5x + -10x2 = -1[-1((-15 + -3x)) + (10x)(10x)]
-16 + -5x + -10x2 = -1[(-15 * -1 + -3x * -1) + (10x)(10x)]
-16 + -5x + -10x2 = -1[(15 + 3x) + (10x)(10x)]

Remove parenthesis around (10x)
-16 + -5x + -10x2 = -1[15 + 3x + 10x(10x)]

Remove parenthesis around (10x)
-16 + -5x + -10x2 = -1[15 + 3x + 10x * 10x]

Reorder the terms for easier multiplication:
-16 + -5x + -10x2 = -1[15 + 3x + 10 * 10x * x]

Multiply 10 * 10
-16 + -5x + -10x2 = -1[15 + 3x + 100x * x]

Multiply x * x
-16 + -5x + -10x2 = -1[15 + 3x + 100x2]
-16 + -5x + -10x2 = [15 * -1 + 3x * -1 + 100x2 * -1]
-16 + -5x + -10x2 = [-15 + -3x + -100x2]

Solving
-16 + -5x + -10x2 = -15 + -3x + -100x2

Solving for variable 'x'.

Reorder the terms:
-16 + 15 + -5x + 3x + -10x2 + 100x2 = -15 + -3x + -100x2 + 15 + 3x + 100x2

Combine like terms: -16 + 15 = -1
-1 + -5x + 3x + -10x2 + 100x2 = -15 + -3x + -100x2 + 15 + 3x + 100x2

Combine like terms: -5x + 3x = -2x
-1 + -2x + -10x2 + 100x2 = -15 + -3x + -100x2 + 15 + 3x + 100x2

Combine like terms: -10x2 + 100x2 = 90x2
-1 + -2x + 90x2 = -15 + -3x + -100x2 + 15 + 3x + 100x2

Reorder the terms:
-1 + -2x + 90x2 = -15 + 15 + -3x + 3x + -100x2 + 100x2

Combine like terms: -15 + 15 = 0
-1 + -2x + 90x2 = 0 + -3x + 3x + -100x2 + 100x2
-1 + -2x + 90x2 = -3x + 3x + -100x2 + 100x2

Combine like terms: -3x + 3x = 0
-1 + -2x + 90x2 = 0 + -100x2 + 100x2
-1 + -2x + 90x2 = -100x2 + 100x2

Combine like terms: -100x2 + 100x2 = 0
-1 + -2x + 90x2 = 0

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

Divide each side by '90'.
-0.01111111111 + -0.02222222222x + x2 = 0

Move the constant term to the right:

Add '0.01111111111' to each side of the equation.
-0.01111111111 + -0.02222222222x + 0.01111111111 + x2 = 0 + 0.01111111111

Reorder the terms:
-0.01111111111 + 0.01111111111 + -0.02222222222x + x2 = 0 + 0.01111111111

Combine like terms: -0.01111111111 + 0.01111111111 = 0.00000000000
0.00000000000 + -0.02222222222x + x2 = 0 + 0.01111111111
-0.02222222222x + x2 = 0 + 0.01111111111

Combine like terms: 0 + 0.01111111111 = 0.01111111111
-0.02222222222x + x2 = 0.01111111111

The x term is -0.02222222222x.  Take half its coefficient (-0.01111111111).
Square it (0.0001234567901) and add it to both sides.

Add '0.0001234567901' to each side of the equation.
-0.02222222222x + 0.0001234567901 + x2 = 0.01111111111 + 0.0001234567901

Reorder the terms:
0.0001234567901 + -0.02222222222x + x2 = 0.01111111111 + 0.0001234567901

Combine like terms: 0.01111111111 + 0.0001234567901 = 0.0112345679001
0.0001234567901 + -0.02222222222x + x2 = 0.0112345679001

Factor a perfect square on the left side:
(x + -0.01111111111)(x + -0.01111111111) = 0.0112345679001

Calculate the square root of the right side: 0.105993245

Break this problem into two subproblems by setting 
(x + -0.01111111111) equal to 0.105993245 and -0.105993245.


Subproblem 1
x + -0.01111111111 = 0.105993245

Simplifying
x + -0.01111111111 = 0.105993245

Reorder the terms:
-0.01111111111 + x = 0.105993245

Solving
-0.01111111111 + x = 0.105993245

Solving for variable 'x'.

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

Add '0.01111111111' to each side of the equation.
-0.01111111111 + 0.01111111111 + x = 0.105993245 + 0.01111111111

Combine like terms: -0.01111111111 + 0.01111111111 = 0.00000000000
0.00000000000 + x = 0.105993245 + 0.01111111111
x = 0.105993245 + 0.01111111111

Combine like terms: 0.105993245 + 0.01111111111 = 0.11710435611
x = 0.11710435611

Simplifying
x = 0.11710435611


Subproblem 2
x + -0.01111111111 = -0.105993245

Simplifying
x + -0.01111111111 = -0.105993245

Reorder the terms:
-0.01111111111 + x = -0.105993245

Solving
-0.01111111111 + x = -0.105993245

Solving for variable 'x'.

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

Add '0.01111111111' to each side of the equation.
-0.01111111111 + 0.01111111111 + x = -0.105993245 + 0.01111111111

Combine like terms: -0.01111111111 + 0.01111111111 = 0.00000000000
0.00000000000 + x = -0.105993245 + 0.01111111111
x = -0.105993245 + 0.01111111111

Combine like terms: -0.105993245 + 0.01111111111 = -0.09488213389
x = -0.09488213389

Simplifying
x = -0.09488213389


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.11710435611, -0.09488213389}

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