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

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


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

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

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

Multiply (5 + 2x) * (-1 + 5x)
(5(-1 + 5x) + 2x * (-1 + 5x)) = 0
((-1 * 5 + 5x * 5) + 2x * (-1 + 5x)) = 0
((-5 + 25x) + 2x * (-1 + 5x)) = 0
(-5 + 25x + (-1 * 2x + 5x * 2x)) = 0
(-5 + 25x + (-2x + 10x2)) = 0

Combine like terms: 25x + -2x = 23x
(-5 + 23x + 10x2) = 0

Solving
-5 + 23x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -2x)(1 + -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 '(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 = {-2.5, 0.2}

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