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

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


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

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

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

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

Combine like terms: 8x + -9x = -1x
(12 + -1x + -6x2) = 0

Solving
12 + -1x + -6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {1.333333333, -1.5}

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