(3x+5)(14x-6)=0

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Solution for (3x+5)(14x-6)=0 equation: 


Simplifying
(3x + 5)(14x + -6) = 0

Reorder the terms:
(5 + 3x)(14x + -6) = 0

Reorder the terms:
(5 + 3x)(-6 + 14x) = 0

Multiply (5 + 3x) * (-6 + 14x)
(5(-6 + 14x) + 3x * (-6 + 14x)) = 0
((-6 * 5 + 14x * 5) + 3x * (-6 + 14x)) = 0
((-30 + 70x) + 3x * (-6 + 14x)) = 0
(-30 + 70x + (-6 * 3x + 14x * 3x)) = 0
(-30 + 70x + (-18x + 42x2)) = 0

Combine like terms: 70x + -18x = 52x
(-30 + 52x + 42x2) = 0

Solving
-30 + 52x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 26x + 21x2) = 0

Factor a trinomial.
2((-5 + -3x)(3 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-1.666666667, 0.4285714286}

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