=4+(3x-6)(x+7)

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Solution for =4+(3x-6)(x+7) equation:


Simplifying
0 = 4 + (3x + -6)(x + 7)

Reorder the terms:
0 = 4 + (-6 + 3x)(x + 7)

Reorder the terms:
0 = 4 + (-6 + 3x)(7 + x)

Multiply (-6 + 3x) * (7 + x)
0 = 4 + (-6(7 + x) + 3x * (7 + x))
0 = 4 + ((7 * -6 + x * -6) + 3x * (7 + x))
0 = 4 + ((-42 + -6x) + 3x * (7 + x))
0 = 4 + (-42 + -6x + (7 * 3x + x * 3x))
0 = 4 + (-42 + -6x + (21x + 3x2))

Combine like terms: -6x + 21x = 15x
0 = 4 + (-42 + 15x + 3x2)

Combine like terms: 4 + -42 = -38
0 = -38 + 15x + 3x2

Solving
0 = -38 + 15x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 38 = 38
38 + -15x + -3x2 = -38 + 15x + 3x2 + 38 + -15x + -3x2

Reorder the terms:
38 + -15x + -3x2 = -38 + 38 + 15x + -15x + 3x2 + -3x2

Combine like terms: -38 + 38 = 0
38 + -15x + -3x2 = 0 + 15x + -15x + 3x2 + -3x2
38 + -15x + -3x2 = 15x + -15x + 3x2 + -3x2

Combine like terms: 15x + -15x = 0
38 + -15x + -3x2 = 0 + 3x2 + -3x2
38 + -15x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
38 + -15x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-12.66666667 + 5x + x2 = 0

Move the constant term to the right:

Add '12.66666667' to each side of the equation.
-12.66666667 + 5x + 12.66666667 + x2 = 0 + 12.66666667

Reorder the terms:
-12.66666667 + 12.66666667 + 5x + x2 = 0 + 12.66666667

Combine like terms: -12.66666667 + 12.66666667 = 0.00000000
0.00000000 + 5x + x2 = 0 + 12.66666667
5x + x2 = 0 + 12.66666667

Combine like terms: 0 + 12.66666667 = 12.66666667
5x + x2 = 12.66666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 12.66666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 12.66666667 + 6.25

Combine like terms: 12.66666667 + 6.25 = 18.91666667
6.25 + 5x + x2 = 18.91666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 18.91666667

Calculate the square root of the right side: 4.349329451

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.349329451 and -4.349329451.

Subproblem 1

x + 2.5 = 4.349329451 Simplifying x + 2.5 = 4.349329451 Reorder the terms: 2.5 + x = 4.349329451 Solving 2.5 + x = 4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.349329451 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.349329451 + -2.5 x = 4.349329451 + -2.5 Combine like terms: 4.349329451 + -2.5 = 1.849329451 x = 1.849329451 Simplifying x = 1.849329451

Subproblem 2

x + 2.5 = -4.349329451 Simplifying x + 2.5 = -4.349329451 Reorder the terms: 2.5 + x = -4.349329451 Solving 2.5 + x = -4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.349329451 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.349329451 + -2.5 x = -4.349329451 + -2.5 Combine like terms: -4.349329451 + -2.5 = -6.849329451 x = -6.849329451 Simplifying x = -6.849329451

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.849329451, -6.849329451}

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