=(7x^2+3)(4)-(4x-7)(14x+3)

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Solution for =(7x^2+3)(4)-(4x-7)(14x+3) equation:


Simplifying
0 = (7x2 + 3)(4) + -1(4x + -7)(14x + 3)

Reorder the terms:
0 = (3 + 7x2)(4) + -1(4x + -7)(14x + 3)

Reorder the terms for easier multiplication:
0 = 4(3 + 7x2) + -1(4x + -7)(14x + 3)
0 = (3 * 4 + 7x2 * 4) + -1(4x + -7)(14x + 3)
0 = (12 + 28x2) + -1(4x + -7)(14x + 3)

Reorder the terms:
0 = 12 + 28x2 + -1(-7 + 4x)(14x + 3)

Reorder the terms:
0 = 12 + 28x2 + -1(-7 + 4x)(3 + 14x)

Multiply (-7 + 4x) * (3 + 14x)
0 = 12 + 28x2 + -1(-7(3 + 14x) + 4x * (3 + 14x))
0 = 12 + 28x2 + -1((3 * -7 + 14x * -7) + 4x * (3 + 14x))
0 = 12 + 28x2 + -1((-21 + -98x) + 4x * (3 + 14x))
0 = 12 + 28x2 + -1(-21 + -98x + (3 * 4x + 14x * 4x))
0 = 12 + 28x2 + -1(-21 + -98x + (12x + 56x2))

Combine like terms: -98x + 12x = -86x
0 = 12 + 28x2 + -1(-21 + -86x + 56x2)
0 = 12 + 28x2 + (-21 * -1 + -86x * -1 + 56x2 * -1)
0 = 12 + 28x2 + (21 + 86x + -56x2)

Reorder the terms:
0 = 12 + 21 + 86x + 28x2 + -56x2

Combine like terms: 12 + 21 = 33
0 = 33 + 86x + 28x2 + -56x2

Combine like terms: 28x2 + -56x2 = -28x2
0 = 33 + 86x + -28x2

Solving
0 = 33 + 86x + -28x2

Solving for variable 'x'.

Combine like terms: 0 + -33 = -33
-33 + -86x + 28x2 = 33 + 86x + -28x2 + -33 + -86x + 28x2

Reorder the terms:
-33 + -86x + 28x2 = 33 + -33 + 86x + -86x + -28x2 + 28x2

Combine like terms: 33 + -33 = 0
-33 + -86x + 28x2 = 0 + 86x + -86x + -28x2 + 28x2
-33 + -86x + 28x2 = 86x + -86x + -28x2 + 28x2

Combine like terms: 86x + -86x = 0
-33 + -86x + 28x2 = 0 + -28x2 + 28x2
-33 + -86x + 28x2 = -28x2 + 28x2

Combine like terms: -28x2 + 28x2 = 0
-33 + -86x + 28x2 = 0

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

Divide each side by '28'.
-1.178571429 + -3.071428571x + x2 = 0

Move the constant term to the right:

Add '1.178571429' to each side of the equation.
-1.178571429 + -3.071428571x + 1.178571429 + x2 = 0 + 1.178571429

Reorder the terms:
-1.178571429 + 1.178571429 + -3.071428571x + x2 = 0 + 1.178571429

Combine like terms: -1.178571429 + 1.178571429 = 0.000000000
0.000000000 + -3.071428571x + x2 = 0 + 1.178571429
-3.071428571x + x2 = 0 + 1.178571429

Combine like terms: 0 + 1.178571429 = 1.178571429
-3.071428571x + x2 = 1.178571429

The x term is -3.071428571x.  Take half its coefficient (-1.535714286).
Square it (2.358418368) and add it to both sides.

Add '2.358418368' to each side of the equation.
-3.071428571x + 2.358418368 + x2 = 1.178571429 + 2.358418368

Reorder the terms:
2.358418368 + -3.071428571x + x2 = 1.178571429 + 2.358418368

Combine like terms: 1.178571429 + 2.358418368 = 3.536989797
2.358418368 + -3.071428571x + x2 = 3.536989797

Factor a perfect square on the left side:
(x + -1.535714286)(x + -1.535714286) = 3.536989797

Calculate the square root of the right side: 1.88068865

Break this problem into two subproblems by setting 
(x + -1.535714286) equal to 1.88068865 and -1.88068865.

Subproblem 1

x + -1.535714286 = 1.88068865 Simplifying x + -1.535714286 = 1.88068865 Reorder the terms: -1.535714286 + x = 1.88068865 Solving -1.535714286 + x = 1.88068865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.535714286' to each side of the equation. -1.535714286 + 1.535714286 + x = 1.88068865 + 1.535714286 Combine like terms: -1.535714286 + 1.535714286 = 0.000000000 0.000000000 + x = 1.88068865 + 1.535714286 x = 1.88068865 + 1.535714286 Combine like terms: 1.88068865 + 1.535714286 = 3.416402936 x = 3.416402936 Simplifying x = 3.416402936

Subproblem 2

x + -1.535714286 = -1.88068865 Simplifying x + -1.535714286 = -1.88068865 Reorder the terms: -1.535714286 + x = -1.88068865 Solving -1.535714286 + x = -1.88068865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.535714286' to each side of the equation. -1.535714286 + 1.535714286 + x = -1.88068865 + 1.535714286 Combine like terms: -1.535714286 + 1.535714286 = 0.000000000 0.000000000 + x = -1.88068865 + 1.535714286 x = -1.88068865 + 1.535714286 Combine like terms: -1.88068865 + 1.535714286 = -0.344974364 x = -0.344974364 Simplifying x = -0.344974364

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.416402936, -0.344974364}

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