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

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


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

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

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

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

Combine like terms: -49x + 2x = -47x
-2(-14 + -47x + 7x2) = 0
(-14 * -2 + -47x * -2 + 7x2 * -2) = 0
(28 + 94x + -14x2) = 0

Solving
28 + 94x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 47x + -7x2) = 0

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

Ignore the factor 2.

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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 = {7, -0.2857142857}

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