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

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


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

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

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

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

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

Solving
8 + 22x + 15x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-0.8, -0.6666666667}

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