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

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


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

Reorder the terms:
8x(7 + x) = 6(x + -4)
(7 * 8x + x * 8x) = 6(x + -4)
(56x + 8x2) = 6(x + -4)

Reorder the terms:
56x + 8x2 = 6(-4 + x)
56x + 8x2 = (-4 * 6 + x * 6)
56x + 8x2 = (-24 + 6x)

Solving
56x + 8x2 = -24 + 6x

Solving for variable 'x'.

Reorder the terms:
24 + 56x + -6x + 8x2 = -24 + 6x + 24 + -6x

Combine like terms: 56x + -6x = 50x
24 + 50x + 8x2 = -24 + 6x + 24 + -6x

Reorder the terms:
24 + 50x + 8x2 = -24 + 24 + 6x + -6x

Combine like terms: -24 + 24 = 0
24 + 50x + 8x2 = 0 + 6x + -6x
24 + 50x + 8x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
24 + 50x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 25x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(12 + 25x + 4x2)' equal to zero and attempt to solve:

Simplifying
12 + 25x + 4x2 = 0

Solving
12 + 25x + 4x2 = 0

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

Divide each side by '4'.
3 + 6.25x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 6.25x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 6.25x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 6.25x + x2 = 0 + -3
6.25x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
6.25x + x2 = -3

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = -3 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = -3 + 9.765625

Combine like terms: -3 + 9.765625 = 6.765625
9.765625 + 6.25x + x2 = 6.765625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 6.765625

Calculate the square root of the right side: 2.601081506

Break this problem into two subproblems by setting 
(x + 3.125) equal to 2.601081506 and -2.601081506.


Subproblem 1
x + 3.125 = 2.601081506

Simplifying
x + 3.125 = 2.601081506

Reorder the terms:
3.125 + x = 2.601081506

Solving
3.125 + x = 2.601081506

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 2.601081506 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 2.601081506 + -3.125
x = 2.601081506 + -3.125

Combine like terms: 2.601081506 + -3.125 = -0.523918494
x = -0.523918494

Simplifying
x = -0.523918494


Subproblem 2
x + 3.125 = -2.601081506

Simplifying
x + 3.125 = -2.601081506

Reorder the terms:
3.125 + x = -2.601081506

Solving
3.125 + x = -2.601081506

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -2.601081506 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -2.601081506 + -3.125
x = -2.601081506 + -3.125

Combine like terms: -2.601081506 + -3.125 = -5.726081506
x = -5.726081506

Simplifying
x = -5.726081506


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.523918494, -5.726081506}
Solution
x = {-0.523918494, -5.726081506}

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