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

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


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

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

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

Multiply (-6 + 3x) * (7 + 2x)
(-6(7 + 2x) + 3x * (7 + 2x)) = 0
((7 * -6 + 2x * -6) + 3x * (7 + 2x)) = 0
((-42 + -12x) + 3x * (7 + 2x)) = 0
(-42 + -12x + (7 * 3x + 2x * 3x)) = 0
(-42 + -12x + (21x + 6x2)) = 0

Combine like terms: -12x + 21x = 9x
(-42 + 9x + 6x2) = 0

Solving
-42 + 9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 3x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {-3.5, 2}

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