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

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


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

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

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

Multiply (7 + 3x) * (-6 + 2x)
(7(-6 + 2x) + 3x * (-6 + 2x)) = 0
((-6 * 7 + 2x * 7) + 3x * (-6 + 2x)) = 0
((-42 + 14x) + 3x * (-6 + 2x)) = 0
(-42 + 14x + (-6 * 3x + 2x * 3x)) = 0
(-42 + 14x + (-18x + 6x2)) = 0

Combine like terms: 14x + -18x = -4x
(-42 + -4x + 6x2) = 0

Solving
-42 + -4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -2x + 3x2) = 0

Factor a trinomial.
2((-7 + -3x)(3 + -1x)) = 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 '(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
Solution
x = {-2.333333333, 3}

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