(4x+14)(7x-2)=100

Solution for (4x+14)(7x-2)=100 equation:

Simplifying
(4x + 14)(7x + -2) = 100

Reorder the terms:
(14 + 4x)(7x + -2) = 100

Reorder the terms:
(14 + 4x)(-2 + 7x) = 100

Multiply (14 + 4x) * (-2 + 7x)
(14(-2 + 7x) + 4x * (-2 + 7x)) = 100
((-2 * 14 + 7x * 14) + 4x * (-2 + 7x)) = 100
((-28 + 98x) + 4x * (-2 + 7x)) = 100
(-28 + 98x + (-2 * 4x + 7x * 4x)) = 100
(-28 + 98x + (-8x + 28x2)) = 100

Combine like terms: 98x + -8x = 90x
(-28 + 90x + 28x2) = 100

Solving
-28 + 90x + 28x2 = 100

Solving for variable 'x'.

Reorder the terms:
-28 + -100 + 90x + 28x2 = 100 + -100

Combine like terms: -28 + -100 = -128
-128 + 90x + 28x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-128 + 90x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-64 + 45x + 14x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-64 + 45x + 14x2)' equal to zero and attempt to solve:

Simplifying
-64 + 45x + 14x2 = 0

Solving
-64 + 45x + 14x2 = 0

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

Divide each side by '14'.
-4.571428571 + 3.214285714x + x2 = 0

Move the constant term to the right:

Add '4.571428571' to each side of the equation.
-4.571428571 + 3.214285714x + 4.571428571 + x2 = 0 + 4.571428571

Reorder the terms:
-4.571428571 + 4.571428571 + 3.214285714x + x2 = 0 + 4.571428571

Combine like terms: -4.571428571 + 4.571428571 = 0.000000000
0.000000000 + 3.214285714x + x2 = 0 + 4.571428571
3.214285714x + x2 = 0 + 4.571428571

Combine like terms: 0 + 4.571428571 = 4.571428571
3.214285714x + x2 = 4.571428571

The x term is 3.214285714x.  Take half its coefficient (1.607142857).
Square it (2.582908163) and add it to both sides.

Add '2.582908163' to each side of the equation.
3.214285714x + 2.582908163 + x2 = 4.571428571 + 2.582908163

Reorder the terms:
2.582908163 + 3.214285714x + x2 = 4.571428571 + 2.582908163

Combine like terms: 4.571428571 + 2.582908163 = 7.154336734
2.582908163 + 3.214285714x + x2 = 7.154336734

Factor a perfect square on the left side:
(x + 1.607142857)(x + 1.607142857) = 7.154336734

Calculate the square root of the right side: 2.674759192

Break this problem into two subproblems by setting 
(x + 1.607142857) equal to 2.674759192 and -2.674759192.

Subproblem 1
x + 1.607142857 = 2.674759192

Simplifying
x + 1.607142857 = 2.674759192

Reorder the terms:
1.607142857 + x = 2.674759192

Solving
1.607142857 + x = 2.674759192

Solving for variable 'x'.

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

Add '-1.607142857' to each side of the equation.
1.607142857 + -1.607142857 + x = 2.674759192 + -1.607142857

Combine like terms: 1.607142857 + -1.607142857 = 0.000000000
0.000000000 + x = 2.674759192 + -1.607142857
x = 2.674759192 + -1.607142857

Combine like terms: 2.674759192 + -1.607142857 = 1.067616335
x = 1.067616335

Simplifying
x = 1.067616335

Subproblem 2
x + 1.607142857 = -2.674759192

Simplifying
x + 1.607142857 = -2.674759192

Reorder the terms:
1.607142857 + x = -2.674759192

Solving
1.607142857 + x = -2.674759192

Solving for variable 'x'.

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

Add '-1.607142857' to each side of the equation.
1.607142857 + -1.607142857 + x = -2.674759192 + -1.607142857

Combine like terms: 1.607142857 + -1.607142857 = 0.000000000
0.000000000 + x = -2.674759192 + -1.607142857
x = -2.674759192 + -1.607142857

Combine like terms: -2.674759192 + -1.607142857 = -4.281902049
x = -4.281902049

Simplifying
x = -4.281902049

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.067616335, -4.281902049}
Solution
x = {1.067616335, -4.281902049}