(5+x)2-(3x-4)(5+x)=0

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Solution for (5+x)2-(3x-4)(5+x)=0 equation: 


Simplifying
(5 + x) * 2 + -1(3x + -4)(5 + x) = 0

Reorder the terms for easier multiplication:
2(5 + x) + -1(3x + -4)(5 + x) = 0
(5 * 2 + x * 2) + -1(3x + -4)(5 + x) = 0
(10 + 2x) + -1(3x + -4)(5 + x) = 0

Reorder the terms:
10 + 2x + -1(-4 + 3x)(5 + x) = 0

Multiply (-4 + 3x) * (5 + x)
10 + 2x + -1(-4(5 + x) + 3x * (5 + x)) = 0
10 + 2x + -1((5 * -4 + x * -4) + 3x * (5 + x)) = 0
10 + 2x + -1((-20 + -4x) + 3x * (5 + x)) = 0
10 + 2x + -1(-20 + -4x + (5 * 3x + x * 3x)) = 0
10 + 2x + -1(-20 + -4x + (15x + 3x2)) = 0

Combine like terms: -4x + 15x = 11x
10 + 2x + -1(-20 + 11x + 3x2) = 0
10 + 2x + (-20 * -1 + 11x * -1 + 3x2 * -1) = 0
10 + 2x + (20 + -11x + -3x2) = 0

Reorder the terms:
10 + 20 + 2x + -11x + -3x2 = 0

Combine like terms: 10 + 20 = 30
30 + 2x + -11x + -3x2 = 0

Combine like terms: 2x + -11x = -9x
30 + -9x + -3x2 = 0

Solving
30 + -9x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -3x + -1x2) = 0

Factor a trinomial.
3((2 + -1x)(5 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, -5}

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