(7x-3)(x+6)=-2

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Solution for (7x-3)(x+6)=-2 equation:


Simplifying
(7x + -3)(x + 6) = -2

Reorder the terms:
(-3 + 7x)(x + 6) = -2

Reorder the terms:
(-3 + 7x)(6 + x) = -2

Multiply (-3 + 7x) * (6 + x)
(-3(6 + x) + 7x * (6 + x)) = -2
((6 * -3 + x * -3) + 7x * (6 + x)) = -2
((-18 + -3x) + 7x * (6 + x)) = -2
(-18 + -3x + (6 * 7x + x * 7x)) = -2
(-18 + -3x + (42x + 7x2)) = -2

Combine like terms: -3x + 42x = 39x
(-18 + 39x + 7x2) = -2

Solving
-18 + 39x + 7x2 = -2

Solving for variable 'x'.

Reorder the terms:
-18 + 2 + 39x + 7x2 = -2 + 2

Combine like terms: -18 + 2 = -16
-16 + 39x + 7x2 = -2 + 2

Combine like terms: -2 + 2 = 0
-16 + 39x + 7x2 = 0

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

Divide each side by '7'.
-2.285714286 + 5.571428571x + x2 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + 5.571428571x + 2.285714286 + x2 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + 5.571428571x + x2 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + 5.571428571x + x2 = 0 + 2.285714286
5.571428571x + x2 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
5.571428571x + x2 = 2.285714286

The x term is 5.571428571x.  Take half its coefficient (2.785714286).
Square it (7.760204083) and add it to both sides.

Add '7.760204083' to each side of the equation.
5.571428571x + 7.760204083 + x2 = 2.285714286 + 7.760204083

Reorder the terms:
7.760204083 + 5.571428571x + x2 = 2.285714286 + 7.760204083

Combine like terms: 2.285714286 + 7.760204083 = 10.045918369
7.760204083 + 5.571428571x + x2 = 10.045918369

Factor a perfect square on the left side:
(x + 2.785714286)(x + 2.785714286) = 10.045918369

Calculate the square root of the right side: 3.169529676

Break this problem into two subproblems by setting 
(x + 2.785714286) equal to 3.169529676 and -3.169529676.

Subproblem 1

x + 2.785714286 = 3.169529676 Simplifying x + 2.785714286 = 3.169529676 Reorder the terms: 2.785714286 + x = 3.169529676 Solving 2.785714286 + x = 3.169529676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = 3.169529676 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = 3.169529676 + -2.785714286 x = 3.169529676 + -2.785714286 Combine like terms: 3.169529676 + -2.785714286 = 0.38381539 x = 0.38381539 Simplifying x = 0.38381539

Subproblem 2

x + 2.785714286 = -3.169529676 Simplifying x + 2.785714286 = -3.169529676 Reorder the terms: 2.785714286 + x = -3.169529676 Solving 2.785714286 + x = -3.169529676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = -3.169529676 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = -3.169529676 + -2.785714286 x = -3.169529676 + -2.785714286 Combine like terms: -3.169529676 + -2.785714286 = -5.955243962 x = -5.955243962 Simplifying x = -5.955243962

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.38381539, -5.955243962}

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