(2x+5)(4x-9)=0

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Solution for (2x+5)(4x-9)=0 equation: 


Simplifying
(2x + 5)(4x + -9) = 0

Reorder the terms:
(5 + 2x)(4x + -9) = 0

Reorder the terms:
(5 + 2x)(-9 + 4x) = 0

Multiply (5 + 2x) * (-9 + 4x)
(5(-9 + 4x) + 2x * (-9 + 4x)) = 0
((-9 * 5 + 4x * 5) + 2x * (-9 + 4x)) = 0
((-45 + 20x) + 2x * (-9 + 4x)) = 0
(-45 + 20x + (-9 * 2x + 4x * 2x)) = 0
(-45 + 20x + (-18x + 8x2)) = 0

Combine like terms: 20x + -18x = 2x
(-45 + 2x + 8x2) = 0

Solving
-45 + 2x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -2x)(9 + -4x) = 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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-2.5, 2.25}

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