2(4x+1)(3x-2)=0

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Solution for 2(4x+1)(3x-2)=0 equation: 


Simplifying
2(4x + 1)(3x + -2) = 0

Reorder the terms:
2(1 + 4x)(3x + -2) = 0

Reorder the terms:
2(1 + 4x)(-2 + 3x) = 0

Multiply (1 + 4x) * (-2 + 3x)
2(1(-2 + 3x) + 4x * (-2 + 3x)) = 0
2((-2 * 1 + 3x * 1) + 4x * (-2 + 3x)) = 0
2((-2 + 3x) + 4x * (-2 + 3x)) = 0
2(-2 + 3x + (-2 * 4x + 3x * 4x)) = 0
2(-2 + 3x + (-8x + 12x2)) = 0

Combine like terms: 3x + -8x = -5x
2(-2 + -5x + 12x2) = 0
(-2 * 2 + -5x * 2 + 12x2 * 2) = 0
(-4 + -10x + 24x2) = 0

Solving
-4 + -10x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -5x + 12x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

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 = {-0.25, 0.6666666667}

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