(2x-3)(8x+6)=0

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Solution for (2x-3)(8x+6)=0 equation: 


Simplifying
(2x + -3)(8x + 6) = 0

Reorder the terms:
(-3 + 2x)(8x + 6) = 0

Reorder the terms:
(-3 + 2x)(6 + 8x) = 0

Multiply (-3 + 2x) * (6 + 8x)
(-3(6 + 8x) + 2x * (6 + 8x)) = 0
((6 * -3 + 8x * -3) + 2x * (6 + 8x)) = 0
((-18 + -24x) + 2x * (6 + 8x)) = 0
(-18 + -24x + (6 * 2x + 8x * 2x)) = 0
(-18 + -24x + (12x + 16x2)) = 0

Combine like terms: -24x + 12x = -12x
(-18 + -12x + 16x2) = 0

Solving
-18 + -12x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -6x + 8x2) = 0

Factor a trinomial.
2((-3 + -4x)(3 + -2x)) = 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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.75, 1.5}

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