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

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

Simplifying
2(x)(x) + 4(x)(5) = 0

Multiply x * x
2x2 + 4(x)(5) = 0

Reorder the terms for easier multiplication:
2x2 + 4 * 5x = 0

Multiply 4 * 5
2x2 + 20x = 0

Reorder the terms:
20x + 2x2 = 0

Solving
20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(10 + 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {0, -10}