(2x-5)(4x+15)=0

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Solution for (2x-5)(4x+15)=0 equation: 


Simplifying
(2x + -5)(4x + 15) = 0

Reorder the terms:
(-5 + 2x)(4x + 15) = 0

Reorder the terms:
(-5 + 2x)(15 + 4x) = 0

Multiply (-5 + 2x) * (15 + 4x)
(-5(15 + 4x) + 2x * (15 + 4x)) = 0
((15 * -5 + 4x * -5) + 2x * (15 + 4x)) = 0
((-75 + -20x) + 2x * (15 + 4x)) = 0
(-75 + -20x + (15 * 2x + 4x * 2x)) = 0
(-75 + -20x + (30x + 8x2)) = 0

Combine like terms: -20x + 30x = 10x
(-75 + 10x + 8x2) = 0

Solving
-75 + 10x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-15 + -4x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-15 + -4x)' equal to zero and attempt to solve:

Simplifying
-15 + -4x = 0

Solving
-15 + -4x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4x = 0 + 15
-4x = 0 + 15

Combine like terms: 0 + 15 = 15
-4x = 15

Divide each side by '-4'.
x = -3.75

Simplifying
x = -3.75

Subproblem 2
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
Solution
x = {-3.75, 2.5}

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