(2x+3)(4x+5)=0

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Solution for (2x+3)(4x+5)=0 equation: 


Simplifying
(2x + 3)(4x + 5) = 0

Reorder the terms:
(3 + 2x)(4x + 5) = 0

Reorder the terms:
(3 + 2x)(5 + 4x) = 0

Multiply (3 + 2x) * (5 + 4x)
(3(5 + 4x) + 2x * (5 + 4x)) = 0
((5 * 3 + 4x * 3) + 2x * (5 + 4x)) = 0
((15 + 12x) + 2x * (5 + 4x)) = 0
(15 + 12x + (5 * 2x + 4x * 2x)) = 0
(15 + 12x + (10x + 8x2)) = 0

Combine like terms: 12x + 10x = 22x
(15 + 22x + 8x2) = 0

Solving
15 + 22x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 2x)(5 + 4x) = 0


Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, -1.25}

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