(3x+7)(2x-1)=0

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Solution for (3x+7)(2x-1)=0 equation: 


Simplifying
(3x + 7)(2x + -1) = 0

Reorder the terms:
(7 + 3x)(2x + -1) = 0

Reorder the terms:
(7 + 3x)(-1 + 2x) = 0

Multiply (7 + 3x) * (-1 + 2x)
(7(-1 + 2x) + 3x * (-1 + 2x)) = 0
((-1 * 7 + 2x * 7) + 3x * (-1 + 2x)) = 0
((-7 + 14x) + 3x * (-1 + 2x)) = 0
(-7 + 14x + (-1 * 3x + 2x * 3x)) = 0
(-7 + 14x + (-3x + 6x2)) = 0

Combine like terms: 14x + -3x = 11x
(-7 + 11x + 6x2) = 0

Solving
-7 + 11x + 6x2 = 0

Solving for variable 'x'.

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


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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-2.333333333, 0.5}

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