(2x+10)(5x+1)=0

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Solution for (2x+10)(5x+1)=0 equation: 


Simplifying
(2x + 10)(5x + 1) = 0

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

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

Multiply (10 + 2x) * (1 + 5x)
(10(1 + 5x) + 2x * (1 + 5x)) = 0
((1 * 10 + 5x * 10) + 2x * (1 + 5x)) = 0
((10 + 50x) + 2x * (1 + 5x)) = 0
(10 + 50x + (1 * 2x + 5x * 2x)) = 0
(10 + 50x + (2x + 10x2)) = 0

Combine like terms: 50x + 2x = 52x
(10 + 52x + 10x2) = 0

Solving
10 + 52x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 26x + 5x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-5, -0.2}

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