(3x+4)(7x-14)=0

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Solution for (3x+4)(7x-14)=0 equation: 


Simplifying
(3x + 4)(7x + -14) = 0

Reorder the terms:
(4 + 3x)(7x + -14) = 0

Reorder the terms:
(4 + 3x)(-14 + 7x) = 0

Multiply (4 + 3x) * (-14 + 7x)
(4(-14 + 7x) + 3x * (-14 + 7x)) = 0
((-14 * 4 + 7x * 4) + 3x * (-14 + 7x)) = 0
((-56 + 28x) + 3x * (-14 + 7x)) = 0
(-56 + 28x + (-14 * 3x + 7x * 3x)) = 0
(-56 + 28x + (-42x + 21x2)) = 0

Combine like terms: 28x + -42x = -14x
(-56 + -14x + 21x2) = 0

Solving
-56 + -14x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -2x + 3x2) = 0

Factor a trinomial.
7((-4 + -3x)(2 + -1x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
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
Solution
x = {-1.333333333, 2}

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