(x-1)(x+2)-(7x-8)(x+5)=

Solution for (x-1)(x+2)-(7x-8)(x+5)= equation:

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

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

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

Multiply (-1 + x) * (2 + x)
(-1(2 + x) + x(2 + x)) + -1(7x + -8)(x + 5) = 0
((2 * -1 + x * -1) + x(2 + x)) + -1(7x + -8)(x + 5) = 0
((-2 + -1x) + x(2 + x)) + -1(7x + -8)(x + 5) = 0
(-2 + -1x + (2 * x + x * x)) + -1(7x + -8)(x + 5) = 0
(-2 + -1x + (2x + x2)) + -1(7x + -8)(x + 5) = 0

Combine like terms: -1x + 2x = 1x
(-2 + 1x + x2) + -1(7x + -8)(x + 5) = 0

Reorder the terms:
-2 + 1x + x2 + -1(-8 + 7x)(x + 5) = 0

Reorder the terms:
-2 + 1x + x2 + -1(-8 + 7x)(5 + x) = 0

Multiply (-8 + 7x) * (5 + x)
-2 + 1x + x2 + -1(-8(5 + x) + 7x * (5 + x)) = 0
-2 + 1x + x2 + -1((5 * -8 + x * -8) + 7x * (5 + x)) = 0
-2 + 1x + x2 + -1((-40 + -8x) + 7x * (5 + x)) = 0
-2 + 1x + x2 + -1(-40 + -8x + (5 * 7x + x * 7x)) = 0
-2 + 1x + x2 + -1(-40 + -8x + (35x + 7x2)) = 0

Combine like terms: -8x + 35x = 27x
-2 + 1x + x2 + -1(-40 + 27x + 7x2) = 0
-2 + 1x + x2 + (-40 * -1 + 27x * -1 + 7x2 * -1) = 0
-2 + 1x + x2 + (40 + -27x + -7x2) = 0

Reorder the terms:
-2 + 40 + 1x + -27x + x2 + -7x2 = 0

Combine like terms: -2 + 40 = 38
38 + 1x + -27x + x2 + -7x2 = 0

Combine like terms: 1x + -27x = -26x
38 + -26x + x2 + -7x2 = 0

Combine like terms: x2 + -7x2 = -6x2
38 + -26x + -6x2 = 0

Solving
38 + -26x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(19 + -13x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(19 + -13x + -3x2)' equal to zero and attempt to solve:

Simplifying
19 + -13x + -3x2 = 0

Solving
19 + -13x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-6.333333333 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 4.333333333x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 4.333333333x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 4.333333333x + x2 = 0 + 6.333333333
4.333333333x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
4.333333333x + x2 = 6.333333333

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 6.333333333 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 6.333333333 + 4.694444446

Combine like terms: 6.333333333 + 4.694444446 = 11.027777779
4.694444446 + 4.333333333x + x2 = 11.027777779

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 11.027777779

Calculate the square root of the right side: 3.320809808

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 3.320809808 and -3.320809808.

Subproblem 1
x + 2.166666667 = 3.320809808

Simplifying
x + 2.166666667 = 3.320809808

Reorder the terms:
2.166666667 + x = 3.320809808

Solving
2.166666667 + x = 3.320809808

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 3.320809808 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 3.320809808 + -2.166666667
x = 3.320809808 + -2.166666667

Combine like terms: 3.320809808 + -2.166666667 = 1.154143141
x = 1.154143141

Simplifying
x = 1.154143141

Subproblem 2
x + 2.166666667 = -3.320809808

Simplifying
x + 2.166666667 = -3.320809808

Reorder the terms:
2.166666667 + x = -3.320809808

Solving
2.166666667 + x = -3.320809808

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -3.320809808 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -3.320809808 + -2.166666667
x = -3.320809808 + -2.166666667

Combine like terms: -3.320809808 + -2.166666667 = -5.487476475
x = -5.487476475

Simplifying
x = -5.487476475

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.154143141, -5.487476475}
Solution
x = {1.154143141, -5.487476475}