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

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

Simplifying
(3x + -2)(x + 5) + -1(x + -7)(2x + 3) = 0

Reorder the terms:
(-2 + 3x)(x + 5) + -1(x + -7)(2x + 3) = 0

Reorder the terms:
(-2 + 3x)(5 + x) + -1(x + -7)(2x + 3) = 0

Multiply (-2 + 3x) * (5 + x)
(-2(5 + x) + 3x * (5 + x)) + -1(x + -7)(2x + 3) = 0
((5 * -2 + x * -2) + 3x * (5 + x)) + -1(x + -7)(2x + 3) = 0
((-10 + -2x) + 3x * (5 + x)) + -1(x + -7)(2x + 3) = 0
(-10 + -2x + (5 * 3x + x * 3x)) + -1(x + -7)(2x + 3) = 0
(-10 + -2x + (15x + 3x2)) + -1(x + -7)(2x + 3) = 0

Combine like terms: -2x + 15x = 13x
(-10 + 13x + 3x2) + -1(x + -7)(2x + 3) = 0

Reorder the terms:
-10 + 13x + 3x2 + -1(-7 + x)(2x + 3) = 0

Reorder the terms:
-10 + 13x + 3x2 + -1(-7 + x)(3 + 2x) = 0

Multiply (-7 + x) * (3 + 2x)
-10 + 13x + 3x2 + -1(-7(3 + 2x) + x(3 + 2x)) = 0
-10 + 13x + 3x2 + -1((3 * -7 + 2x * -7) + x(3 + 2x)) = 0
-10 + 13x + 3x2 + -1((-21 + -14x) + x(3 + 2x)) = 0
-10 + 13x + 3x2 + -1(-21 + -14x + (3 * x + 2x * x)) = 0
-10 + 13x + 3x2 + -1(-21 + -14x + (3x + 2x2)) = 0

Combine like terms: -14x + 3x = -11x
-10 + 13x + 3x2 + -1(-21 + -11x + 2x2) = 0
-10 + 13x + 3x2 + (-21 * -1 + -11x * -1 + 2x2 * -1) = 0
-10 + 13x + 3x2 + (21 + 11x + -2x2) = 0

Reorder the terms:
-10 + 21 + 13x + 11x + 3x2 + -2x2 = 0

Combine like terms: -10 + 21 = 11
11 + 13x + 11x + 3x2 + -2x2 = 0

Combine like terms: 13x + 11x = 24x
11 + 24x + 3x2 + -2x2 = 0

Combine like terms: 3x2 + -2x2 = 1x2
11 + 24x + 1x2 = 0

Solving
11 + 24x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 24x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 24x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 24x + x2 = 0 + -11
24x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
24x + x2 = -11

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = -11 + 144

Reorder the terms:
144 + 24x + x2 = -11 + 144

Combine like terms: -11 + 144 = 133
144 + 24x + x2 = 133

Factor a perfect square on the left side:
(x + 12)(x + 12) = 133

Calculate the square root of the right side: 11.532562595

Break this problem into two subproblems by setting 
(x + 12) equal to 11.532562595 and -11.532562595.

Subproblem 1
x + 12 = 11.532562595

Simplifying
x + 12 = 11.532562595

Reorder the terms:
12 + x = 11.532562595

Solving
12 + x = 11.532562595

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 11.532562595 + -12

Combine like terms: 12 + -12 = 0
0 + x = 11.532562595 + -12
x = 11.532562595 + -12

Combine like terms: 11.532562595 + -12 = -0.467437405
x = -0.467437405

Simplifying
x = -0.467437405

Subproblem 2
x + 12 = -11.532562595

Simplifying
x + 12 = -11.532562595

Reorder the terms:
12 + x = -11.532562595

Solving
12 + x = -11.532562595

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -11.532562595 + -12

Combine like terms: 12 + -12 = 0
0 + x = -11.532562595 + -12
x = -11.532562595 + -12

Combine like terms: -11.532562595 + -12 = -23.532562595
x = -23.532562595

Simplifying
x = -23.532562595

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.467437405, -23.532562595}