(2x+7)(x-3)=140

Solution for (2x+7)(x-3)=140 equation:

Simplifying
(2x + 7)(x + -3) = 140

Reorder the terms:
(7 + 2x)(x + -3) = 140

Reorder the terms:
(7 + 2x)(-3 + x) = 140

Multiply (7 + 2x) * (-3 + x)
(7(-3 + x) + 2x * (-3 + x)) = 140
((-3 * 7 + x * 7) + 2x * (-3 + x)) = 140
((-21 + 7x) + 2x * (-3 + x)) = 140
(-21 + 7x + (-3 * 2x + x * 2x)) = 140
(-21 + 7x + (-6x + 2x2)) = 140

Combine like terms: 7x + -6x = 1x
(-21 + 1x + 2x2) = 140

Solving
-21 + 1x + 2x2 = 140

Solving for variable 'x'.

Reorder the terms:
-21 + -140 + 1x + 2x2 = 140 + -140

Combine like terms: -21 + -140 = -161
-161 + 1x + 2x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-161 + 1x + 2x2 = 0

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

Divide each side by '2'.
-80.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '80.5' to each side of the equation.
-80.5 + 0.5x + 80.5 + x2 = 0 + 80.5

Reorder the terms:
-80.5 + 80.5 + 0.5x + x2 = 0 + 80.5

Combine like terms: -80.5 + 80.5 = 0.0
0.0 + 0.5x + x2 = 0 + 80.5
0.5x + x2 = 0 + 80.5

Combine like terms: 0 + 80.5 = 80.5
0.5x + x2 = 80.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 80.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 80.5 + 0.0625

Combine like terms: 80.5 + 0.0625 = 80.5625
0.0625 + 0.5x + x2 = 80.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 80.5625

Calculate the square root of the right side: 8.975661536

Break this problem into two subproblems by setting 
(x + 0.25) equal to 8.975661536 and -8.975661536.

Subproblem 1
x + 0.25 = 8.975661536

Simplifying
x + 0.25 = 8.975661536

Reorder the terms:
0.25 + x = 8.975661536

Solving
0.25 + x = 8.975661536

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 8.975661536 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 8.975661536 + -0.25
x = 8.975661536 + -0.25

Combine like terms: 8.975661536 + -0.25 = 8.725661536
x = 8.725661536

Simplifying
x = 8.725661536

Subproblem 2
x + 0.25 = -8.975661536

Simplifying
x + 0.25 = -8.975661536

Reorder the terms:
0.25 + x = -8.975661536

Solving
0.25 + x = -8.975661536

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -8.975661536 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -8.975661536 + -0.25
x = -8.975661536 + -0.25

Combine like terms: -8.975661536 + -0.25 = -9.225661536
x = -9.225661536

Simplifying
x = -9.225661536

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.725661536, -9.225661536}