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

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


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

Reorder the terms:
5x(5 + 2x) + 2(2x + 5) = 0
(5 * 5x + 2x * 5x) + 2(2x + 5) = 0
(25x + 10x2) + 2(2x + 5) = 0

Reorder the terms:
25x + 10x2 + 2(5 + 2x) = 0
25x + 10x2 + (5 * 2 + 2x * 2) = 0
25x + 10x2 + (10 + 4x) = 0

Reorder the terms:
10 + 25x + 4x + 10x2 = 0

Combine like terms: 25x + 4x = 29x
10 + 29x + 10x2 = 0

Solving
10 + 29x + 10x2 = 0

Solving for variable 'x'.

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


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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

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

Simplifying
2 + 5x = 0

Solving
2 + 5x = 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 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-2.5, -0.4}

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