(3x-4)(8x+6)=0

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Solution for (3x-4)(8x+6)=0 equation: 


Simplifying
(3x + -4)(8x + 6) = 0

Reorder the terms:
(-4 + 3x)(8x + 6) = 0

Reorder the terms:
(-4 + 3x)(6 + 8x) = 0

Multiply (-4 + 3x) * (6 + 8x)
(-4(6 + 8x) + 3x * (6 + 8x)) = 0
((6 * -4 + 8x * -4) + 3x * (6 + 8x)) = 0
((-24 + -32x) + 3x * (6 + 8x)) = 0
(-24 + -32x + (6 * 3x + 8x * 3x)) = 0
(-24 + -32x + (18x + 24x2)) = 0

Combine like terms: -32x + 18x = -14x
(-24 + -14x + 24x2) = 0

Solving
-24 + -14x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -7x + 12x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {-0.75, 1.333333333}

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