(x+6)2-(x+3)(x+4)=0

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Solution for (x+6)2-(x+3)(x+4)=0 equation: 


Simplifying
(x + 6) * 2 + -1(x + 3)(x + 4) = 0

Reorder the terms:
(6 + x) * 2 + -1(x + 3)(x + 4) = 0

Reorder the terms for easier multiplication:
2(6 + x) + -1(x + 3)(x + 4) = 0
(6 * 2 + x * 2) + -1(x + 3)(x + 4) = 0
(12 + 2x) + -1(x + 3)(x + 4) = 0

Reorder the terms:
12 + 2x + -1(3 + x)(x + 4) = 0

Reorder the terms:
12 + 2x + -1(3 + x)(4 + x) = 0

Multiply (3 + x) * (4 + x)
12 + 2x + -1(3(4 + x) + x(4 + x)) = 0
12 + 2x + -1((4 * 3 + x * 3) + x(4 + x)) = 0
12 + 2x + -1((12 + 3x) + x(4 + x)) = 0
12 + 2x + -1(12 + 3x + (4 * x + x * x)) = 0
12 + 2x + -1(12 + 3x + (4x + x2)) = 0

Combine like terms: 3x + 4x = 7x
12 + 2x + -1(12 + 7x + x2) = 0
12 + 2x + (12 * -1 + 7x * -1 + x2 * -1) = 0
12 + 2x + (-12 + -7x + -1x2) = 0

Reorder the terms:
12 + -12 + 2x + -7x + -1x2 = 0

Combine like terms: 12 + -12 = 0
0 + 2x + -7x + -1x2 = 0
2x + -7x + -1x2 = 0

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

Solving
-5x + -1x2 = 0

Solving for variable 'x'.

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

Ignore the factor -1.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0, -5}

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