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

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


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

Reorder the terms:
(2 + 5x)(5 + -4x) = 0

Multiply (2 + 5x) * (5 + -4x)
(2(5 + -4x) + 5x * (5 + -4x)) = 0
((5 * 2 + -4x * 2) + 5x * (5 + -4x)) = 0
((10 + -8x) + 5x * (5 + -4x)) = 0
(10 + -8x + (5 * 5x + -4x * 5x)) = 0
(10 + -8x + (25x + -20x2)) = 0

Combine like terms: -8x + 25x = 17x
(10 + 17x + -20x2) = 0

Solving
10 + 17x + -20x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -4x)(2 + 5x) = 0


Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

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 = {1.25, -0.4}

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