(3x-2)(4x-14)=0

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Solution for (3x-2)(4x-14)=0 equation: 


Simplifying
(3x + -2)(4x + -14) = 0

Reorder the terms:
(-2 + 3x)(4x + -14) = 0

Reorder the terms:
(-2 + 3x)(-14 + 4x) = 0

Multiply (-2 + 3x) * (-14 + 4x)
(-2(-14 + 4x) + 3x * (-14 + 4x)) = 0
((-14 * -2 + 4x * -2) + 3x * (-14 + 4x)) = 0
((28 + -8x) + 3x * (-14 + 4x)) = 0
(28 + -8x + (-14 * 3x + 4x * 3x)) = 0
(28 + -8x + (-42x + 12x2)) = 0

Combine like terms: -8x + -42x = -50x
(28 + -50x + 12x2) = 0

Solving
28 + -50x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -25x + 6x2) = 0

Factor a trinomial.
2((2 + -3x)(7 + -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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0.6666666667, 3.5}

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