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

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


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

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

Multiply (3 + 2x) * (4 + 3x)
(3(4 + 3x) + 2x * (4 + 3x)) = 0
((4 * 3 + 3x * 3) + 2x * (4 + 3x)) = 0
((12 + 9x) + 2x * (4 + 3x)) = 0
(12 + 9x + (4 * 2x + 3x * 2x)) = 0
(12 + 9x + (8x + 6x2)) = 0

Combine like terms: 9x + 8x = 17x
(12 + 17x + 6x2) = 0

Solving
12 + 17x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 2x)(4 + 3x) = 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 '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-1.5, -1.333333333}

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