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

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


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

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

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

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

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

Solving
4 + -5x + -6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {0.5, -1.333333333}

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