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

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


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

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

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

Multiply (1 + 3x) * (-3 + 4x)
(1(-3 + 4x) + 3x * (-3 + 4x)) = 0
((-3 * 1 + 4x * 1) + 3x * (-3 + 4x)) = 0
((-3 + 4x) + 3x * (-3 + 4x)) = 0
(-3 + 4x + (-3 * 3x + 4x * 3x)) = 0
(-3 + 4x + (-9x + 12x2)) = 0

Combine like terms: 4x + -9x = -5x
(-3 + -5x + 12x2) = 0

Solving
-3 + -5x + 12x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-0.3333333333, 0.75}

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