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

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


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

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