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

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


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

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

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

Combine like terms: 6x + 8x = 14x
(-4 + 14x + -12x2) = 0

Solving
-4 + 14x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 7x + -6x2) = 0

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

Ignore the factor 2.

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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.6666666667, 0.5}

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