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

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


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

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

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

Multiply (-7 + 3x) * (7 + 2x)
(-7(7 + 2x) + 3x * (7 + 2x)) = 0
((7 * -7 + 2x * -7) + 3x * (7 + 2x)) = 0
((-49 + -14x) + 3x * (7 + 2x)) = 0
(-49 + -14x + (7 * 3x + 2x * 3x)) = 0
(-49 + -14x + (21x + 6x2)) = 0

Combine like terms: -14x + 21x = 7x
(-49 + 7x + 6x2) = 0

Solving
-49 + 7x + 6x2 = 0

Solving for variable 'x'.

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


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 '(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
Solution
x = {-3.5, 2.333333333}

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