-6x(x+4)+7=8x+2(x+5)

Solution for -6x(x+4)+7=8x+2(x+5) equation:

Simplifying
-6x(x + 4) + 7 = 8x + 2(x + 5)

Reorder the terms:
-6x(4 + x) + 7 = 8x + 2(x + 5)
(4 * -6x + x * -6x) + 7 = 8x + 2(x + 5)
(-24x + -6x2) + 7 = 8x + 2(x + 5)

Reorder the terms:
7 + -24x + -6x2 = 8x + 2(x + 5)

Reorder the terms:
7 + -24x + -6x2 = 8x + 2(5 + x)
7 + -24x + -6x2 = 8x + (5 * 2 + x * 2)
7 + -24x + -6x2 = 8x + (10 + 2x)

Reorder the terms:
7 + -24x + -6x2 = 10 + 8x + 2x

Combine like terms: 8x + 2x = 10x
7 + -24x + -6x2 = 10 + 10x

Solving
7 + -24x + -6x2 = 10 + 10x

Solving for variable 'x'.

Reorder the terms:
7 + -10 + -24x + -10x + -6x2 = 10 + 10x + -10 + -10x

Combine like terms: 7 + -10 = -3
-3 + -24x + -10x + -6x2 = 10 + 10x + -10 + -10x

Combine like terms: -24x + -10x = -34x
-3 + -34x + -6x2 = 10 + 10x + -10 + -10x

Reorder the terms:
-3 + -34x + -6x2 = 10 + -10 + 10x + -10x

Combine like terms: 10 + -10 = 0
-3 + -34x + -6x2 = 0 + 10x + -10x
-3 + -34x + -6x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-3 + -34x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 34x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 34x + 6x2)' equal to zero and attempt to solve:

Simplifying
3 + 34x + 6x2 = 0

Solving
3 + 34x + 6x2 = 0

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

Divide each side by '6'.
0.5 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 5.666666667x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 5.666666667x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 5.666666667x + x2 = 0 + -0.5
5.666666667x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
5.666666667x + x2 = -0.5

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = -0.5 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -0.5 + 8.027777782

Combine like terms: -0.5 + 8.027777782 = 7.527777782
8.027777782 + 5.666666667x + x2 = 7.527777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 7.527777782

Calculate the square root of the right side: 2.743679606

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 2.743679606 and -2.743679606.

Subproblem 1
x + 2.833333334 = 2.743679606

Simplifying
x + 2.833333334 = 2.743679606

Reorder the terms:
2.833333334 + x = 2.743679606

Solving
2.833333334 + x = 2.743679606

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 2.743679606 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 2.743679606 + -2.833333334
x = 2.743679606 + -2.833333334

Combine like terms: 2.743679606 + -2.833333334 = -0.089653728
x = -0.089653728

Simplifying
x = -0.089653728

Subproblem 2
x + 2.833333334 = -2.743679606

Simplifying
x + 2.833333334 = -2.743679606

Reorder the terms:
2.833333334 + x = -2.743679606

Solving
2.833333334 + x = -2.743679606

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -2.743679606 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -2.743679606 + -2.833333334
x = -2.743679606 + -2.833333334

Combine like terms: -2.743679606 + -2.833333334 = -5.57701294
x = -5.57701294

Simplifying
x = -5.57701294

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.089653728, -5.57701294}
Solution
x = {-0.089653728, -5.57701294}