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

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


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

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

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

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

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

Solving
-20 + 17x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -2x)(4 + -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 '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

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

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

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-2.5, 0.8}

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