(3x+4)(2x-1)=0

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Solution for (3x+4)(2x-1)=0 equation: 


Simplifying
(3x + 4)(2x + -1) = 0

Reorder the terms:
(4 + 3x)(2x + -1) = 0

Reorder the terms:
(4 + 3x)(-1 + 2x) = 0

Multiply (4 + 3x) * (-1 + 2x)
(4(-1 + 2x) + 3x * (-1 + 2x)) = 0
((-1 * 4 + 2x * 4) + 3x * (-1 + 2x)) = 0
((-4 + 8x) + 3x * (-1 + 2x)) = 0
(-4 + 8x + (-1 * 3x + 2x * 3x)) = 0
(-4 + 8x + (-3x + 6x2)) = 0

Combine like terms: 8x + -3x = 5x
(-4 + 5x + 6x2) = 0

Solving
-4 + 5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 0.5}

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