2(7x-2)(3x+7)=0

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Solution for 2(7x-2)(3x+7)=0 equation: 


Simplifying
2(7x + -2)(3x + 7) = 0

Reorder the terms:
2(-2 + 7x)(3x + 7) = 0

Reorder the terms:
2(-2 + 7x)(7 + 3x) = 0

Multiply (-2 + 7x) * (7 + 3x)
2(-2(7 + 3x) + 7x * (7 + 3x)) = 0
2((7 * -2 + 3x * -2) + 7x * (7 + 3x)) = 0
2((-14 + -6x) + 7x * (7 + 3x)) = 0
2(-14 + -6x + (7 * 7x + 3x * 7x)) = 0
2(-14 + -6x + (49x + 21x2)) = 0

Combine like terms: -6x + 49x = 43x
2(-14 + 43x + 21x2) = 0
(-14 * 2 + 43x * 2 + 21x2 * 2) = 0
(-28 + 86x + 42x2) = 0

Solving
-28 + 86x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 43x + 21x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 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 + -3x = 0 + 7

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

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

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

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

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

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

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

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-2.333333333, 0.2857142857}

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