-6(x-3)(2x+7)=0

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Solution for -6(x-3)(2x+7)=0 equation: 


Simplifying
-6(x + -3)(2x + 7) = 0

Reorder the terms:
-6(-3 + x)(2x + 7) = 0

Reorder the terms:
-6(-3 + x)(7 + 2x) = 0

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

Combine like terms: -6x + 7x = 1x
-6(-21 + 1x + 2x2) = 0
(-21 * -6 + 1x * -6 + 2x2 * -6) = 0
(126 + -6x + -12x2) = 0

Solving
126 + -6x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(21 + -1x + -2x2) = 0

Factor a trinomial.
6((3 + -1x)(7 + 2x)) = 0

Ignore the factor 6.

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
7 + 2x = 0

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

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

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

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {3, -3.5}

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