(4x+8)(3x-2)=0

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Solution for (4x+8)(3x-2)=0 equation: 


Simplifying
(4x + 8)(3x + -2) = 0

Reorder the terms:
(8 + 4x)(3x + -2) = 0

Reorder the terms:
(8 + 4x)(-2 + 3x) = 0

Multiply (8 + 4x) * (-2 + 3x)
(8(-2 + 3x) + 4x * (-2 + 3x)) = 0
((-2 * 8 + 3x * 8) + 4x * (-2 + 3x)) = 0
((-16 + 24x) + 4x * (-2 + 3x)) = 0
(-16 + 24x + (-2 * 4x + 3x * 4x)) = 0
(-16 + 24x + (-8x + 12x2)) = 0

Combine like terms: 24x + -8x = 16x
(-16 + 16x + 12x2) = 0

Solving
-16 + 16x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 4x + 3x2) = 0

Factor a trinomial.
4((-2 + -1x)(2 + -3x)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 0.6666666667}

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