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

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


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

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

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

Multiply (-4 + 6x) * (4 + 8x)
(-4(4 + 8x) + 6x * (4 + 8x)) = 0
((4 * -4 + 8x * -4) + 6x * (4 + 8x)) = 0
((-16 + -32x) + 6x * (4 + 8x)) = 0
(-16 + -32x + (4 * 6x + 8x * 6x)) = 0
(-16 + -32x + (24x + 48x2)) = 0

Combine like terms: -32x + 24x = -8x
(-16 + -8x + 48x2) = 0

Solving
-16 + -8x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -1x + 6x2) = 0

Factor a trinomial.
8((-1 + -2x)(2 + -3x)) = 0

Ignore the factor 8.

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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-0.5, 0.6666666667}

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