0=(4x+2)(7x+5)-(8x-14)(6x-6)

Solution for 0=(4x+2)(7x+5)-(8x-14)(6x-6) equation:

Simplifying
0 = (4x + 2)(7x + 5) + -1(8x + -14)(6x + -6)

Reorder the terms:
0 = (2 + 4x)(7x + 5) + -1(8x + -14)(6x + -6)

Reorder the terms:
0 = (2 + 4x)(5 + 7x) + -1(8x + -14)(6x + -6)

Multiply (2 + 4x) * (5 + 7x)
0 = (2(5 + 7x) + 4x * (5 + 7x)) + -1(8x + -14)(6x + -6)
0 = ((5 * 2 + 7x * 2) + 4x * (5 + 7x)) + -1(8x + -14)(6x + -6)
0 = ((10 + 14x) + 4x * (5 + 7x)) + -1(8x + -14)(6x + -6)
0 = (10 + 14x + (5 * 4x + 7x * 4x)) + -1(8x + -14)(6x + -6)
0 = (10 + 14x + (20x + 28x2)) + -1(8x + -14)(6x + -6)

Combine like terms: 14x + 20x = 34x
0 = (10 + 34x + 28x2) + -1(8x + -14)(6x + -6)

Reorder the terms:
0 = 10 + 34x + 28x2 + -1(-14 + 8x)(6x + -6)

Reorder the terms:
0 = 10 + 34x + 28x2 + -1(-14 + 8x)(-6 + 6x)

Multiply (-14 + 8x) * (-6 + 6x)
0 = 10 + 34x + 28x2 + -1(-14(-6 + 6x) + 8x * (-6 + 6x))
0 = 10 + 34x + 28x2 + -1((-6 * -14 + 6x * -14) + 8x * (-6 + 6x))
0 = 10 + 34x + 28x2 + -1((84 + -84x) + 8x * (-6 + 6x))
0 = 10 + 34x + 28x2 + -1(84 + -84x + (-6 * 8x + 6x * 8x))
0 = 10 + 34x + 28x2 + -1(84 + -84x + (-48x + 48x2))

Combine like terms: -84x + -48x = -132x
0 = 10 + 34x + 28x2 + -1(84 + -132x + 48x2)
0 = 10 + 34x + 28x2 + (84 * -1 + -132x * -1 + 48x2 * -1)
0 = 10 + 34x + 28x2 + (-84 + 132x + -48x2)

Reorder the terms:
0 = 10 + -84 + 34x + 132x + 28x2 + -48x2

Combine like terms: 10 + -84 = -74
0 = -74 + 34x + 132x + 28x2 + -48x2

Combine like terms: 34x + 132x = 166x
0 = -74 + 166x + 28x2 + -48x2

Combine like terms: 28x2 + -48x2 = -20x2
0 = -74 + 166x + -20x2

Solving
0 = -74 + 166x + -20x2

Solving for variable 'x'.

Combine like terms: 0 + 74 = 74
74 + -166x + 20x2 = -74 + 166x + -20x2 + 74 + -166x + 20x2

Reorder the terms:
74 + -166x + 20x2 = -74 + 74 + 166x + -166x + -20x2 + 20x2

Combine like terms: -74 + 74 = 0
74 + -166x + 20x2 = 0 + 166x + -166x + -20x2 + 20x2
74 + -166x + 20x2 = 166x + -166x + -20x2 + 20x2

Combine like terms: 166x + -166x = 0
74 + -166x + 20x2 = 0 + -20x2 + 20x2
74 + -166x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
74 + -166x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(37 + -83x + 10x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(37 + -83x + 10x2)' equal to zero and attempt to solve:

Simplifying
37 + -83x + 10x2 = 0

Solving
37 + -83x + 10x2 = 0

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

Divide each side by '10'.
3.7 + -8.3x + x2 = 0.0

Move the constant term to the right:

Add '-3.7' to each side of the equation.
3.7 + -8.3x + -3.7 + x2 = 0.0 + -3.7

Reorder the terms:
3.7 + -3.7 + -8.3x + x2 = 0.0 + -3.7

Combine like terms: 3.7 + -3.7 = 0.0
0.0 + -8.3x + x2 = 0.0 + -3.7
-8.3x + x2 = 0.0 + -3.7

Combine like terms: 0.0 + -3.7 = -3.7
-8.3x + x2 = -3.7

The x term is -8.3x.  Take half its coefficient (-4.15).
Square it (17.2225) and add it to both sides.

Add '17.2225' to each side of the equation.
-8.3x + 17.2225 + x2 = -3.7 + 17.2225

Reorder the terms:
17.2225 + -8.3x + x2 = -3.7 + 17.2225

Combine like terms: -3.7 + 17.2225 = 13.5225
17.2225 + -8.3x + x2 = 13.5225

Factor a perfect square on the left side:
(x + -4.15)(x + -4.15) = 13.5225

Calculate the square root of the right side: 3.677295202

Break this problem into two subproblems by setting 
(x + -4.15) equal to 3.677295202 and -3.677295202.

Subproblem 1
x + -4.15 = 3.677295202

Simplifying
x + -4.15 = 3.677295202

Reorder the terms:
-4.15 + x = 3.677295202

Solving
-4.15 + x = 3.677295202

Solving for variable 'x'.

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

Add '4.15' to each side of the equation.
-4.15 + 4.15 + x = 3.677295202 + 4.15

Combine like terms: -4.15 + 4.15 = 0.00
0.00 + x = 3.677295202 + 4.15
x = 3.677295202 + 4.15

Combine like terms: 3.677295202 + 4.15 = 7.827295202
x = 7.827295202

Simplifying
x = 7.827295202

Subproblem 2
x + -4.15 = -3.677295202

Simplifying
x + -4.15 = -3.677295202

Reorder the terms:
-4.15 + x = -3.677295202

Solving
-4.15 + x = -3.677295202

Solving for variable 'x'.

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

Add '4.15' to each side of the equation.
-4.15 + 4.15 + x = -3.677295202 + 4.15

Combine like terms: -4.15 + 4.15 = 0.00
0.00 + x = -3.677295202 + 4.15
x = -3.677295202 + 4.15

Combine like terms: -3.677295202 + 4.15 = 0.472704798
x = 0.472704798

Simplifying
x = 0.472704798

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.827295202, 0.472704798}
Solution
x = {7.827295202, 0.472704798}