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

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


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

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

Multiply (-5 + -2x) * (2 + 5x)
(-5(2 + 5x) + -2x * (2 + 5x)) = 0
((2 * -5 + 5x * -5) + -2x * (2 + 5x)) = 0
((-10 + -25x) + -2x * (2 + 5x)) = 0
(-10 + -25x + (2 * -2x + 5x * -2x)) = 0
(-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 out the Greatest Common Factor (GCF), '-1'.
-1(10 + 29x + 10x2) = 0

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

Ignore the factor -1.

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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