(6x-2)(x+7)=0

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Solution for (6x-2)(x+7)=0 equation: 


Simplifying
(6x + -2)(x + 7) = 0

Reorder the terms:
(-2 + 6x)(x + 7) = 0

Reorder the terms:
(-2 + 6x)(7 + x) = 0

Multiply (-2 + 6x) * (7 + x)
(-2(7 + x) + 6x * (7 + x)) = 0
((7 * -2 + x * -2) + 6x * (7 + x)) = 0
((-14 + -2x) + 6x * (7 + x)) = 0
(-14 + -2x + (7 * 6x + x * 6x)) = 0
(-14 + -2x + (42x + 6x2)) = 0

Combine like terms: -2x + 42x = 40x
(-14 + 40x + 6x2) = 0

Solving
-14 + 40x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 20x + 3x2) = 0

Factor a trinomial.
2((-7 + -1x)(1 + -3x)) = 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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-7, 0.3333333333}

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