(x-3)(x+4)-(5x-1)(x+7)=

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Solution for (x-3)(x+4)-(5x-1)(x+7)= equation: 


Simplifying
(x + -3)(x + 4) + -1(5x + -1)(x + 7) = 0

Reorder the terms:
(-3 + x)(x + 4) + -1(5x + -1)(x + 7) = 0

Reorder the terms:
(-3 + x)(4 + x) + -1(5x + -1)(x + 7) = 0

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) + -1(5x + -1)(x + 7) = 0
((4 * -3 + x * -3) + x(4 + x)) + -1(5x + -1)(x + 7) = 0
((-12 + -3x) + x(4 + x)) + -1(5x + -1)(x + 7) = 0
(-12 + -3x + (4 * x + x * x)) + -1(5x + -1)(x + 7) = 0
(-12 + -3x + (4x + x2)) + -1(5x + -1)(x + 7) = 0

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) + -1(5x + -1)(x + 7) = 0

Reorder the terms:
-12 + 1x + x2 + -1(-1 + 5x)(x + 7) = 0

Reorder the terms:
-12 + 1x + x2 + -1(-1 + 5x)(7 + x) = 0

Multiply (-1 + 5x) * (7 + x)
-12 + 1x + x2 + -1(-1(7 + x) + 5x * (7 + x)) = 0
-12 + 1x + x2 + -1((7 * -1 + x * -1) + 5x * (7 + x)) = 0
-12 + 1x + x2 + -1((-7 + -1x) + 5x * (7 + x)) = 0
-12 + 1x + x2 + -1(-7 + -1x + (7 * 5x + x * 5x)) = 0
-12 + 1x + x2 + -1(-7 + -1x + (35x + 5x2)) = 0

Combine like terms: -1x + 35x = 34x
-12 + 1x + x2 + -1(-7 + 34x + 5x2) = 0
-12 + 1x + x2 + (-7 * -1 + 34x * -1 + 5x2 * -1) = 0
-12 + 1x + x2 + (7 + -34x + -5x2) = 0

Reorder the terms:
-12 + 7 + 1x + -34x + x2 + -5x2 = 0

Combine like terms: -12 + 7 = -5
-5 + 1x + -34x + x2 + -5x2 = 0

Combine like terms: 1x + -34x = -33x
-5 + -33x + x2 + -5x2 = 0

Combine like terms: x2 + -5x2 = -4x2
-5 + -33x + -4x2 = 0

Solving
-5 + -33x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 33x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 33x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + 33x + 4x2 = 0

Solving
5 + 33x + 4x2 = 0

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

Divide each side by '4'.
1.25 + 8.25x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 8.25x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 8.25x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 8.25x + x2 = 0 + -1.25
8.25x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
8.25x + x2 = -1.25

The x term is 8.25x.  Take half its coefficient (4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
8.25x + 17.015625 + x2 = -1.25 + 17.015625

Reorder the terms:
17.015625 + 8.25x + x2 = -1.25 + 17.015625

Combine like terms: -1.25 + 17.015625 = 15.765625
17.015625 + 8.25x + x2 = 15.765625

Factor a perfect square on the left side:
(x + 4.125)(x + 4.125) = 15.765625

Calculate the square root of the right side: 3.970595044

Break this problem into two subproblems by setting 
(x + 4.125) equal to 3.970595044 and -3.970595044.


Subproblem 1
x + 4.125 = 3.970595044

Simplifying
x + 4.125 = 3.970595044

Reorder the terms:
4.125 + x = 3.970595044

Solving
4.125 + x = 3.970595044

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = 3.970595044 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = 3.970595044 + -4.125
x = 3.970595044 + -4.125

Combine like terms: 3.970595044 + -4.125 = -0.154404956
x = -0.154404956

Simplifying
x = -0.154404956


Subproblem 2
x + 4.125 = -3.970595044

Simplifying
x + 4.125 = -3.970595044

Reorder the terms:
4.125 + x = -3.970595044

Solving
4.125 + x = -3.970595044

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = -3.970595044 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = -3.970595044 + -4.125
x = -3.970595044 + -4.125

Combine like terms: -3.970595044 + -4.125 = -8.095595044
x = -8.095595044

Simplifying
x = -8.095595044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.154404956, -8.095595044}
Solution
x = {-0.154404956, -8.095595044}

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