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

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


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

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

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

Multiply (2 + 3x) * (-7 + 2x)
(2(-7 + 2x) + 3x * (-7 + 2x)) = 0
((-7 * 2 + 2x * 2) + 3x * (-7 + 2x)) = 0
((-14 + 4x) + 3x * (-7 + 2x)) = 0
(-14 + 4x + (-7 * 3x + 2x * 3x)) = 0
(-14 + 4x + (-21x + 6x2)) = 0

Combine like terms: 4x + -21x = -17x
(-14 + -17x + 6x2) = 0

Solving
-14 + -17x + 6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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 = {-0.6666666667, 3.5}

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