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

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


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

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

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

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

Combine like terms: 2x + -12x = -10x
(8 + -10x + -3x2) = 0

Solving
8 + -10x + -3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {0.6666666667, -4}

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