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

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


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

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

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

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

Solving
10 + -17x + -20x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {0.4, -1.25}

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