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

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


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

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

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

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

Combine like terms: 12x + -4x = 8x
(-8 + 8x + 6x2) = 0

Solving
-8 + 8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 4x + 3x2) = 0

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

Ignore the factor 2.

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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