5x-(x-3)+2=7(2x+1)(x+4)-16

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Solution for 5x-(x-3)+2=7(2x+1)(x+4)-16 equation: 


Simplifying
5x + -1(x + -3) + 2 = 7(2x + 1)(x + 4) + -16

Reorder the terms:
5x + -1(-3 + x) + 2 = 7(2x + 1)(x + 4) + -16
5x + (-3 * -1 + x * -1) + 2 = 7(2x + 1)(x + 4) + -16
5x + (3 + -1x) + 2 = 7(2x + 1)(x + 4) + -16

Reorder the terms:
3 + 2 + 5x + -1x = 7(2x + 1)(x + 4) + -16

Combine like terms: 3 + 2 = 5
5 + 5x + -1x = 7(2x + 1)(x + 4) + -16

Combine like terms: 5x + -1x = 4x
5 + 4x = 7(2x + 1)(x + 4) + -16

Reorder the terms:
5 + 4x = 7(1 + 2x)(x + 4) + -16

Reorder the terms:
5 + 4x = 7(1 + 2x)(4 + x) + -16

Multiply (1 + 2x) * (4 + x)
5 + 4x = 7(1(4 + x) + 2x * (4 + x)) + -16
5 + 4x = 7((4 * 1 + x * 1) + 2x * (4 + x)) + -16
5 + 4x = 7((4 + 1x) + 2x * (4 + x)) + -16
5 + 4x = 7(4 + 1x + (4 * 2x + x * 2x)) + -16
5 + 4x = 7(4 + 1x + (8x + 2x2)) + -16

Combine like terms: 1x + 8x = 9x
5 + 4x = 7(4 + 9x + 2x2) + -16
5 + 4x = (4 * 7 + 9x * 7 + 2x2 * 7) + -16
5 + 4x = (28 + 63x + 14x2) + -16

Reorder the terms:
5 + 4x = 28 + -16 + 63x + 14x2

Combine like terms: 28 + -16 = 12
5 + 4x = 12 + 63x + 14x2

Solving
5 + 4x = 12 + 63x + 14x2

Solving for variable 'x'.

Reorder the terms:
5 + -12 + 4x + -63x + -14x2 = 12 + 63x + 14x2 + -12 + -63x + -14x2

Combine like terms: 5 + -12 = -7
-7 + 4x + -63x + -14x2 = 12 + 63x + 14x2 + -12 + -63x + -14x2

Combine like terms: 4x + -63x = -59x
-7 + -59x + -14x2 = 12 + 63x + 14x2 + -12 + -63x + -14x2

Reorder the terms:
-7 + -59x + -14x2 = 12 + -12 + 63x + -63x + 14x2 + -14x2

Combine like terms: 12 + -12 = 0
-7 + -59x + -14x2 = 0 + 63x + -63x + 14x2 + -14x2
-7 + -59x + -14x2 = 63x + -63x + 14x2 + -14x2

Combine like terms: 63x + -63x = 0
-7 + -59x + -14x2 = 0 + 14x2 + -14x2
-7 + -59x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
-7 + -59x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 59x + 14x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 59x + 14x2)' equal to zero and attempt to solve:

Simplifying
7 + 59x + 14x2 = 0

Solving
7 + 59x + 14x2 = 0

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

Divide each side by '14'.
0.5 + 4.214285714x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 4.214285714x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 4.214285714x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 4.214285714x + x2 = 0 + -0.5
4.214285714x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
4.214285714x + x2 = -0.5

The x term is 4.214285714x.  Take half its coefficient (2.107142857).
Square it (4.440051020) and add it to both sides.

Add '4.440051020' to each side of the equation.
4.214285714x + 4.440051020 + x2 = -0.5 + 4.440051020

Reorder the terms:
4.440051020 + 4.214285714x + x2 = -0.5 + 4.440051020

Combine like terms: -0.5 + 4.440051020 = 3.94005102
4.440051020 + 4.214285714x + x2 = 3.94005102

Factor a perfect square on the left side:
(x + 2.107142857)(x + 2.107142857) = 3.94005102

Calculate the square root of the right side: 1.984956176

Break this problem into two subproblems by setting 
(x + 2.107142857) equal to 1.984956176 and -1.984956176.


Subproblem 1
x + 2.107142857 = 1.984956176

Simplifying
x + 2.107142857 = 1.984956176

Reorder the terms:
2.107142857 + x = 1.984956176

Solving
2.107142857 + x = 1.984956176

Solving for variable 'x'.

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

Add '-2.107142857' to each side of the equation.
2.107142857 + -2.107142857 + x = 1.984956176 + -2.107142857

Combine like terms: 2.107142857 + -2.107142857 = 0.000000000
0.000000000 + x = 1.984956176 + -2.107142857
x = 1.984956176 + -2.107142857

Combine like terms: 1.984956176 + -2.107142857 = -0.122186681
x = -0.122186681

Simplifying
x = -0.122186681


Subproblem 2
x + 2.107142857 = -1.984956176

Simplifying
x + 2.107142857 = -1.984956176

Reorder the terms:
2.107142857 + x = -1.984956176

Solving
2.107142857 + x = -1.984956176

Solving for variable 'x'.

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

Add '-2.107142857' to each side of the equation.
2.107142857 + -2.107142857 + x = -1.984956176 + -2.107142857

Combine like terms: 2.107142857 + -2.107142857 = 0.000000000
0.000000000 + x = -1.984956176 + -2.107142857
x = -1.984956176 + -2.107142857

Combine like terms: -1.984956176 + -2.107142857 = -4.092099033
x = -4.092099033

Simplifying
x = -4.092099033


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.122186681, -4.092099033}
Solution
x = {-0.122186681, -4.092099033}

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