(3x-4)(8x+3)=0

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Solution for (3x-4)(8x+3)=0 equation: 


Simplifying
(3x + -4)(8x + 3) = 0

Reorder the terms:
(-4 + 3x)(8x + 3) = 0

Reorder the terms:
(-4 + 3x)(3 + 8x) = 0

Multiply (-4 + 3x) * (3 + 8x)
(-4(3 + 8x) + 3x * (3 + 8x)) = 0
((3 * -4 + 8x * -4) + 3x * (3 + 8x)) = 0
((-12 + -32x) + 3x * (3 + 8x)) = 0
(-12 + -32x + (3 * 3x + 8x * 3x)) = 0
(-12 + -32x + (9x + 24x2)) = 0

Combine like terms: -32x + 9x = -23x
(-12 + -23x + 24x2) = 0

Solving
-12 + -23x + 24x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -8x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-3 + -8x)' equal to zero and attempt to solve:

Simplifying
-3 + -8x = 0

Solving
-3 + -8x = 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 + -8x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8x = 0 + 3
-8x = 0 + 3

Combine like terms: 0 + 3 = 3
-8x = 3

Divide each side by '-8'.
x = -0.375

Simplifying
x = -0.375

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 = {-0.375, 1.333333333}

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