2(x+5)(x-5)+10+8(x+5)=0

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Solution for 2(x+5)(x-5)+10+8(x+5)=0 equation: 


Simplifying
2(x + 5)(x + -5) + 10 + 8(x + 5) = 0

Reorder the terms:
2(5 + x)(x + -5) + 10 + 8(x + 5) = 0

Reorder the terms:
2(5 + x)(-5 + x) + 10 + 8(x + 5) = 0

Multiply (5 + x) * (-5 + x)
2(5(-5 + x) + x(-5 + x)) + 10 + 8(x + 5) = 0
2((-5 * 5 + x * 5) + x(-5 + x)) + 10 + 8(x + 5) = 0
2((-25 + 5x) + x(-5 + x)) + 10 + 8(x + 5) = 0
2(-25 + 5x + (-5 * x + x * x)) + 10 + 8(x + 5) = 0
2(-25 + 5x + (-5x + x2)) + 10 + 8(x + 5) = 0

Combine like terms: 5x + -5x = 0
2(-25 + 0 + x2) + 10 + 8(x + 5) = 0
2(-25 + x2) + 10 + 8(x + 5) = 0
(-25 * 2 + x2 * 2) + 10 + 8(x + 5) = 0
(-50 + 2x2) + 10 + 8(x + 5) = 0

Reorder the terms:
-50 + 2x2 + 10 + 8(5 + x) = 0
-50 + 2x2 + 10 + (5 * 8 + x * 8) = 0
-50 + 2x2 + 10 + (40 + 8x) = 0

Reorder the terms:
-50 + 10 + 40 + 8x + 2x2 = 0

Combine like terms: -50 + 10 = -40
-40 + 40 + 8x + 2x2 = 0

Combine like terms: -40 + 40 = 0
0 + 8x + 2x2 = 0
8x + 2x2 = 0

Solving
8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(4 + x) = 0

Ignore the factor 2.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {0, -4}

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