(5x-1)(2x-3)=17-(10x+1)(x+6)

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Solution for (5x-1)(2x-3)=17-(10x+1)(x+6) equation: 


Simplifying
(5x + -1)(2x + -3) = 17 + -1(10x + 1)(x + 6)

Reorder the terms:
(-1 + 5x)(2x + -3) = 17 + -1(10x + 1)(x + 6)

Reorder the terms:
(-1 + 5x)(-3 + 2x) = 17 + -1(10x + 1)(x + 6)

Multiply (-1 + 5x) * (-3 + 2x)
(-1(-3 + 2x) + 5x * (-3 + 2x)) = 17 + -1(10x + 1)(x + 6)
((-3 * -1 + 2x * -1) + 5x * (-3 + 2x)) = 17 + -1(10x + 1)(x + 6)
((3 + -2x) + 5x * (-3 + 2x)) = 17 + -1(10x + 1)(x + 6)
(3 + -2x + (-3 * 5x + 2x * 5x)) = 17 + -1(10x + 1)(x + 6)
(3 + -2x + (-15x + 10x2)) = 17 + -1(10x + 1)(x + 6)

Combine like terms: -2x + -15x = -17x
(3 + -17x + 10x2) = 17 + -1(10x + 1)(x + 6)

Reorder the terms:
3 + -17x + 10x2 = 17 + -1(1 + 10x)(x + 6)

Reorder the terms:
3 + -17x + 10x2 = 17 + -1(1 + 10x)(6 + x)

Multiply (1 + 10x) * (6 + x)
3 + -17x + 10x2 = 17 + -1(1(6 + x) + 10x * (6 + x))
3 + -17x + 10x2 = 17 + -1((6 * 1 + x * 1) + 10x * (6 + x))
3 + -17x + 10x2 = 17 + -1((6 + 1x) + 10x * (6 + x))
3 + -17x + 10x2 = 17 + -1(6 + 1x + (6 * 10x + x * 10x))
3 + -17x + 10x2 = 17 + -1(6 + 1x + (60x + 10x2))

Combine like terms: 1x + 60x = 61x
3 + -17x + 10x2 = 17 + -1(6 + 61x + 10x2)
3 + -17x + 10x2 = 17 + (6 * -1 + 61x * -1 + 10x2 * -1)
3 + -17x + 10x2 = 17 + (-6 + -61x + -10x2)

Combine like terms: 17 + -6 = 11
3 + -17x + 10x2 = 11 + -61x + -10x2

Solving
3 + -17x + 10x2 = 11 + -61x + -10x2

Solving for variable 'x'.

Reorder the terms:
3 + -11 + -17x + 61x + 10x2 + 10x2 = 11 + -61x + -10x2 + -11 + 61x + 10x2

Combine like terms: 3 + -11 = -8
-8 + -17x + 61x + 10x2 + 10x2 = 11 + -61x + -10x2 + -11 + 61x + 10x2

Combine like terms: -17x + 61x = 44x
-8 + 44x + 10x2 + 10x2 = 11 + -61x + -10x2 + -11 + 61x + 10x2

Combine like terms: 10x2 + 10x2 = 20x2
-8 + 44x + 20x2 = 11 + -61x + -10x2 + -11 + 61x + 10x2

Reorder the terms:
-8 + 44x + 20x2 = 11 + -11 + -61x + 61x + -10x2 + 10x2

Combine like terms: 11 + -11 = 0
-8 + 44x + 20x2 = 0 + -61x + 61x + -10x2 + 10x2
-8 + 44x + 20x2 = -61x + 61x + -10x2 + 10x2

Combine like terms: -61x + 61x = 0
-8 + 44x + 20x2 = 0 + -10x2 + 10x2
-8 + 44x + 20x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-8 + 44x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 11x + 5x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + 11x + 5x2)' equal to zero and attempt to solve:

Simplifying
-2 + 11x + 5x2 = 0

Solving
-2 + 11x + 5x2 = 0

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

Divide each side by '5'.
-0.4 + 2.2x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 2.2x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 2.2x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 2.2x + x2 = 0 + 0.4
2.2x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
2.2x + x2 = 0.4

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = 0.4 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 0.4 + 1.21

Combine like terms: 0.4 + 1.21 = 1.61
1.21 + 2.2x + x2 = 1.61

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 1.61

Calculate the square root of the right side: 1.268857754

Break this problem into two subproblems by setting 
(x + 1.1) equal to 1.268857754 and -1.268857754.


Subproblem 1
x + 1.1 = 1.268857754

Simplifying
x + 1.1 = 1.268857754

Reorder the terms:
1.1 + x = 1.268857754

Solving
1.1 + x = 1.268857754

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = 1.268857754 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = 1.268857754 + -1.1
x = 1.268857754 + -1.1

Combine like terms: 1.268857754 + -1.1 = 0.168857754
x = 0.168857754

Simplifying
x = 0.168857754


Subproblem 2
x + 1.1 = -1.268857754

Simplifying
x + 1.1 = -1.268857754

Reorder the terms:
1.1 + x = -1.268857754

Solving
1.1 + x = -1.268857754

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = -1.268857754 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = -1.268857754 + -1.1
x = -1.268857754 + -1.1

Combine like terms: -1.268857754 + -1.1 = -2.368857754
x = -2.368857754

Simplifying
x = -2.368857754


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.168857754, -2.368857754}
Solution
x = {0.168857754, -2.368857754}

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