14-5(5x-1)(2x+3)=17-(10x+1)(x-6)

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Solution for 14-5(5x-1)(2x+3)=17-(10x+1)(x-6) equation: 


Simplifying
14 + -5(5x + -1)(2x + 3) = 17 + -1(10x + 1)(x + -6)

Reorder the terms:
14 + -5(-1 + 5x)(2x + 3) = 17 + -1(10x + 1)(x + -6)

Reorder the terms:
14 + -5(-1 + 5x)(3 + 2x) = 17 + -1(10x + 1)(x + -6)

Multiply (-1 + 5x) * (3 + 2x)
14 + -5(-1(3 + 2x) + 5x * (3 + 2x)) = 17 + -1(10x + 1)(x + -6)
14 + -5((3 * -1 + 2x * -1) + 5x * (3 + 2x)) = 17 + -1(10x + 1)(x + -6)
14 + -5((-3 + -2x) + 5x * (3 + 2x)) = 17 + -1(10x + 1)(x + -6)
14 + -5(-3 + -2x + (3 * 5x + 2x * 5x)) = 17 + -1(10x + 1)(x + -6)
14 + -5(-3 + -2x + (15x + 10x2)) = 17 + -1(10x + 1)(x + -6)

Combine like terms: -2x + 15x = 13x
14 + -5(-3 + 13x + 10x2) = 17 + -1(10x + 1)(x + -6)
14 + (-3 * -5 + 13x * -5 + 10x2 * -5) = 17 + -1(10x + 1)(x + -6)
14 + (15 + -65x + -50x2) = 17 + -1(10x + 1)(x + -6)

Combine like terms: 14 + 15 = 29
29 + -65x + -50x2 = 17 + -1(10x + 1)(x + -6)

Reorder the terms:
29 + -65x + -50x2 = 17 + -1(1 + 10x)(x + -6)

Reorder the terms:
29 + -65x + -50x2 = 17 + -1(1 + 10x)(-6 + x)

Multiply (1 + 10x) * (-6 + x)
29 + -65x + -50x2 = 17 + -1(1(-6 + x) + 10x * (-6 + x))
29 + -65x + -50x2 = 17 + -1((-6 * 1 + x * 1) + 10x * (-6 + x))
29 + -65x + -50x2 = 17 + -1((-6 + 1x) + 10x * (-6 + x))
29 + -65x + -50x2 = 17 + -1(-6 + 1x + (-6 * 10x + x * 10x))
29 + -65x + -50x2 = 17 + -1(-6 + 1x + (-60x + 10x2))

Combine like terms: 1x + -60x = -59x
29 + -65x + -50x2 = 17 + -1(-6 + -59x + 10x2)
29 + -65x + -50x2 = 17 + (-6 * -1 + -59x * -1 + 10x2 * -1)
29 + -65x + -50x2 = 17 + (6 + 59x + -10x2)

Combine like terms: 17 + 6 = 23
29 + -65x + -50x2 = 23 + 59x + -10x2

Solving
29 + -65x + -50x2 = 23 + 59x + -10x2

Solving for variable 'x'.

Reorder the terms:
29 + -23 + -65x + -59x + -50x2 + 10x2 = 23 + 59x + -10x2 + -23 + -59x + 10x2

Combine like terms: 29 + -23 = 6
6 + -65x + -59x + -50x2 + 10x2 = 23 + 59x + -10x2 + -23 + -59x + 10x2

Combine like terms: -65x + -59x = -124x
6 + -124x + -50x2 + 10x2 = 23 + 59x + -10x2 + -23 + -59x + 10x2

Combine like terms: -50x2 + 10x2 = -40x2
6 + -124x + -40x2 = 23 + 59x + -10x2 + -23 + -59x + 10x2

Reorder the terms:
6 + -124x + -40x2 = 23 + -23 + 59x + -59x + -10x2 + 10x2

Combine like terms: 23 + -23 = 0
6 + -124x + -40x2 = 0 + 59x + -59x + -10x2 + 10x2
6 + -124x + -40x2 = 59x + -59x + -10x2 + 10x2

Combine like terms: 59x + -59x = 0
6 + -124x + -40x2 = 0 + -10x2 + 10x2
6 + -124x + -40x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
6 + -124x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -62x + -20x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -62x + -20x2)' equal to zero and attempt to solve:

Simplifying
3 + -62x + -20x2 = 0

Solving
3 + -62x + -20x2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-0.15 + 3.1x + x2 = 0.0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 3.1x + 0.15 + x2 = 0.0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 3.1x + x2 = 0.0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 3.1x + x2 = 0.0 + 0.15
3.1x + x2 = 0.0 + 0.15

Combine like terms: 0.0 + 0.15 = 0.15
3.1x + x2 = 0.15

The x term is 3.1x.  Take half its coefficient (1.55).
Square it (2.4025) and add it to both sides.

Add '2.4025' to each side of the equation.
3.1x + 2.4025 + x2 = 0.15 + 2.4025

Reorder the terms:
2.4025 + 3.1x + x2 = 0.15 + 2.4025

Combine like terms: 0.15 + 2.4025 = 2.5525
2.4025 + 3.1x + x2 = 2.5525

Factor a perfect square on the left side:
(x + 1.55)(x + 1.55) = 2.5525

Calculate the square root of the right side: 1.597654531

Break this problem into two subproblems by setting 
(x + 1.55) equal to 1.597654531 and -1.597654531.


Subproblem 1
x + 1.55 = 1.597654531

Simplifying
x + 1.55 = 1.597654531

Reorder the terms:
1.55 + x = 1.597654531

Solving
1.55 + x = 1.597654531

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = 1.597654531 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = 1.597654531 + -1.55
x = 1.597654531 + -1.55

Combine like terms: 1.597654531 + -1.55 = 0.047654531
x = 0.047654531

Simplifying
x = 0.047654531


Subproblem 2
x + 1.55 = -1.597654531

Simplifying
x + 1.55 = -1.597654531

Reorder the terms:
1.55 + x = -1.597654531

Solving
1.55 + x = -1.597654531

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = -1.597654531 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = -1.597654531 + -1.55
x = -1.597654531 + -1.55

Combine like terms: -1.597654531 + -1.55 = -3.147654531
x = -3.147654531

Simplifying
x = -3.147654531


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.047654531, -3.147654531}
Solution
x = {0.047654531, -3.147654531}

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