(5x-6)(x+7)=(1x-2x)(x-14)

Solution for (5x-6)(x+7)=(1x-2x)(x-14) equation:

Simplifying
(5x + -6)(x + 7) = (1x + -2x)(x + -14)

Reorder the terms:
(-6 + 5x)(x + 7) = (1x + -2x)(x + -14)

Reorder the terms:
(-6 + 5x)(7 + x) = (1x + -2x)(x + -14)

Multiply (-6 + 5x) * (7 + x)
(-6(7 + x) + 5x * (7 + x)) = (1x + -2x)(x + -14)
((7 * -6 + x * -6) + 5x * (7 + x)) = (1x + -2x)(x + -14)
((-42 + -6x) + 5x * (7 + x)) = (1x + -2x)(x + -14)
(-42 + -6x + (7 * 5x + x * 5x)) = (1x + -2x)(x + -14)
(-42 + -6x + (35x + 5x2)) = (1x + -2x)(x + -14)

Combine like terms: -6x + 35x = 29x
(-42 + 29x + 5x2) = (1x + -2x)(x + -14)

Combine like terms: 1x + -2x = -1x
-42 + 29x + 5x2 = (-1x)(x + -14)

Remove parenthesis around (-1x)
-42 + 29x + 5x2 = -1x(x + -14)

Reorder the terms:
-42 + 29x + 5x2 = -1x(-14 + x)
-42 + 29x + 5x2 = (-14 * -1x + x * -1x)
-42 + 29x + 5x2 = (14x + -1x2)

Solving
-42 + 29x + 5x2 = 14x + -1x2

Solving for variable 'x'.

Reorder the terms:
-42 + 29x + -14x + 5x2 + x2 = 14x + -1x2 + -14x + x2

Combine like terms: 29x + -14x = 15x
-42 + 15x + 5x2 + x2 = 14x + -1x2 + -14x + x2

Combine like terms: 5x2 + x2 = 6x2
-42 + 15x + 6x2 = 14x + -1x2 + -14x + x2

Reorder the terms:
-42 + 15x + 6x2 = 14x + -14x + -1x2 + x2

Combine like terms: 14x + -14x = 0
-42 + 15x + 6x2 = 0 + -1x2 + x2
-42 + 15x + 6x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-42 + 15x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-14 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-14 + 5x + 2x2 = 0

Solving
-14 + 5x + 2x2 = 0

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

Divide each side by '2'.
-7 + 2.5x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 2.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 2.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2.5x + x2 = 0 + 7
2.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
2.5x + x2 = 7

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 7 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 7 + 1.5625

Combine like terms: 7 + 1.5625 = 8.5625
1.5625 + 2.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.926174978 and -2.926174978.

Subproblem 1
x + 1.25 = 2.926174978

Simplifying
x + 1.25 = 2.926174978

Reorder the terms:
1.25 + x = 2.926174978

Solving
1.25 + x = 2.926174978

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.926174978 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.926174978 + -1.25
x = 2.926174978 + -1.25

Combine like terms: 2.926174978 + -1.25 = 1.676174978
x = 1.676174978

Simplifying
x = 1.676174978

Subproblem 2
x + 1.25 = -2.926174978

Simplifying
x + 1.25 = -2.926174978

Reorder the terms:
1.25 + x = -2.926174978

Solving
1.25 + x = -2.926174978

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.926174978 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.926174978 + -1.25
x = -2.926174978 + -1.25

Combine like terms: -2.926174978 + -1.25 = -4.176174978
x = -4.176174978

Simplifying
x = -4.176174978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.676174978, -4.176174978}
Solution
x = {1.676174978, -4.176174978}