=(2x-5)(3x+8)+7

Solution for =(2x-5)(3x+8)+7 equation:

Simplifying
0 = (2x + -5)(3x + 8) + 7

Reorder the terms:
0 = (-5 + 2x)(3x + 8) + 7

Reorder the terms:
0 = (-5 + 2x)(8 + 3x) + 7

Multiply (-5 + 2x) * (8 + 3x)
0 = (-5(8 + 3x) + 2x * (8 + 3x)) + 7
0 = ((8 * -5 + 3x * -5) + 2x * (8 + 3x)) + 7
0 = ((-40 + -15x) + 2x * (8 + 3x)) + 7
0 = (-40 + -15x + (8 * 2x + 3x * 2x)) + 7
0 = (-40 + -15x + (16x + 6x2)) + 7

Combine like terms: -15x + 16x = 1x
0 = (-40 + 1x + 6x2) + 7

Reorder the terms:
0 = -40 + 7 + 1x + 6x2

Combine like terms: -40 + 7 = -33
0 = -33 + 1x + 6x2

Solving
0 = -33 + 1x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 33 = 33
33 + -1x + -6x2 = -33 + 1x + 6x2 + 33 + -1x + -6x2

Reorder the terms:
33 + -1x + -6x2 = -33 + 33 + 1x + -1x + 6x2 + -6x2

Combine like terms: -33 + 33 = 0
33 + -1x + -6x2 = 0 + 1x + -1x + 6x2 + -6x2
33 + -1x + -6x2 = 1x + -1x + 6x2 + -6x2

Combine like terms: 1x + -1x = 0
33 + -1x + -6x2 = 0 + 6x2 + -6x2
33 + -1x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
33 + -1x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-5.5 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 0.1666666667x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 0.1666666667x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 0.1666666667x + x2 = 0 + 5.5
0.1666666667x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
0.1666666667x + x2 = 5.5

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 5.5 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 5.5 + 0.006944444447

Combine like terms: 5.5 + 0.006944444447 = 5.506944444447
0.006944444447 + 0.1666666667x + x2 = 5.506944444447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 5.506944444447

Calculate the square root of the right side: 2.346687973

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 2.346687973 and -2.346687973.

Subproblem 1
x + 0.08333333335 = 2.346687973

Simplifying
x + 0.08333333335 = 2.346687973

Reorder the terms:
0.08333333335 + x = 2.346687973

Solving
0.08333333335 + x = 2.346687973

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 2.346687973 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 2.346687973 + -0.08333333335
x = 2.346687973 + -0.08333333335

Combine like terms: 2.346687973 + -0.08333333335 = 2.26335463965
x = 2.26335463965

Simplifying
x = 2.26335463965

Subproblem 2
x + 0.08333333335 = -2.346687973

Simplifying
x + 0.08333333335 = -2.346687973

Reorder the terms:
0.08333333335 + x = -2.346687973

Solving
0.08333333335 + x = -2.346687973

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -2.346687973 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -2.346687973 + -0.08333333335
x = -2.346687973 + -0.08333333335

Combine like terms: -2.346687973 + -0.08333333335 = -2.43002130635
x = -2.43002130635

Simplifying
x = -2.43002130635

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.26335463965, -2.43002130635}