(x+3)(x-2)+(x+2)-3x-10=0

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Solution for (x+3)(x-2)+(x+2)-3x-10=0 equation:


Simplifying
(x + 3)(x + -2) + (x + 2) + -3x + -10 = 0

Reorder the terms:
(3 + x)(x + -2) + (x + 2) + -3x + -10 = 0

Reorder the terms:
(3 + x)(-2 + x) + (x + 2) + -3x + -10 = 0

Multiply (3 + x) * (-2 + x)
(3(-2 + x) + x(-2 + x)) + (x + 2) + -3x + -10 = 0
((-2 * 3 + x * 3) + x(-2 + x)) + (x + 2) + -3x + -10 = 0
((-6 + 3x) + x(-2 + x)) + (x + 2) + -3x + -10 = 0
(-6 + 3x + (-2 * x + x * x)) + (x + 2) + -3x + -10 = 0
(-6 + 3x + (-2x + x2)) + (x + 2) + -3x + -10 = 0

Combine like terms: 3x + -2x = 1x
(-6 + 1x + x2) + (x + 2) + -3x + -10 = 0

Reorder the terms:
-6 + 1x + x2 + (2 + x) + -3x + -10 = 0

Remove parenthesis around (2 + x)
-6 + 1x + x2 + 2 + x + -3x + -10 = 0

Reorder the terms:
-6 + 2 + -10 + 1x + x + -3x + x2 = 0

Combine like terms: -6 + 2 = -4
-4 + -10 + 1x + x + -3x + x2 = 0

Combine like terms: -4 + -10 = -14
-14 + 1x + x + -3x + x2 = 0

Combine like terms: 1x + x = 2x
-14 + 2x + -3x + x2 = 0

Combine like terms: 2x + -3x = -1x
-14 + -1x + x2 = 0

Solving
-14 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -1x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -1x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x + x2 = 0 + 14
-1x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-1x + x2 = 14

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 14 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 14 + 0.25

Combine like terms: 14 + 0.25 = 14.25
0.25 + -1x + x2 = 14.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + -0.5 = 3.774917218 Simplifying x + -0.5 = 3.774917218 Reorder the terms: -0.5 + x = 3.774917218 Solving -0.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.774917218 + 0.5 x = 3.774917218 + 0.5 Combine like terms: 3.774917218 + 0.5 = 4.274917218 x = 4.274917218 Simplifying x = 4.274917218

Subproblem 2

x + -0.5 = -3.774917218 Simplifying x + -0.5 = -3.774917218 Reorder the terms: -0.5 + x = -3.774917218 Solving -0.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.774917218 + 0.5 x = -3.774917218 + 0.5 Combine like terms: -3.774917218 + 0.5 = -3.274917218 x = -3.274917218 Simplifying x = -3.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.274917218, -3.274917218}

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