(x-6)(x+8)=-3(x-14)

Solution for (x-6)(x+8)=-3(x-14) equation:

Simplifying
(x + -6)(x + 8) = -3(x + -14)

Reorder the terms:
(-6 + x)(x + 8) = -3(x + -14)

Reorder the terms:
(-6 + x)(8 + x) = -3(x + -14)

Multiply (-6 + x) * (8 + x)
(-6(8 + x) + x(8 + x)) = -3(x + -14)
((8 * -6 + x * -6) + x(8 + x)) = -3(x + -14)
((-48 + -6x) + x(8 + x)) = -3(x + -14)
(-48 + -6x + (8 * x + x * x)) = -3(x + -14)
(-48 + -6x + (8x + x2)) = -3(x + -14)

Combine like terms: -6x + 8x = 2x
(-48 + 2x + x2) = -3(x + -14)

Reorder the terms:
-48 + 2x + x2 = -3(-14 + x)
-48 + 2x + x2 = (-14 * -3 + x * -3)
-48 + 2x + x2 = (42 + -3x)

Solving
-48 + 2x + x2 = 42 + -3x

Solving for variable 'x'.

Reorder the terms:
-48 + -42 + 2x + 3x + x2 = 42 + -3x + -42 + 3x

Combine like terms: -48 + -42 = -90
-90 + 2x + 3x + x2 = 42 + -3x + -42 + 3x

Combine like terms: 2x + 3x = 5x
-90 + 5x + x2 = 42 + -3x + -42 + 3x

Reorder the terms:
-90 + 5x + x2 = 42 + -42 + -3x + 3x

Combine like terms: 42 + -42 = 0
-90 + 5x + x2 = 0 + -3x + 3x
-90 + 5x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-90 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 5x + x2 = 0 + 90
5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
5x + x2 = 90

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 = 90 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 90 + 6.25

Combine like terms: 90 + 6.25 = 96.25
6.25 + 5x + x2 = 96.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.810708435 and -9.810708435.

Subproblem 1
x + 2.5 = 9.810708435

Simplifying
x + 2.5 = 9.810708435

Reorder the terms:
2.5 + x = 9.810708435

Solving
2.5 + x = 9.810708435

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 = 9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.810708435 + -2.5
x = 9.810708435 + -2.5

Combine like terms: 9.810708435 + -2.5 = 7.310708435
x = 7.310708435

Simplifying
x = 7.310708435

Subproblem 2
x + 2.5 = -9.810708435

Simplifying
x + 2.5 = -9.810708435

Reorder the terms:
2.5 + x = -9.810708435

Solving
2.5 + x = -9.810708435

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 = -9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.810708435 + -2.5
x = -9.810708435 + -2.5

Combine like terms: -9.810708435 + -2.5 = -12.310708435
x = -12.310708435

Simplifying
x = -12.310708435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.310708435, -12.310708435}