(4x+6)(2x-8)=0

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Solution for (4x+6)(2x-8)=0 equation: 


Simplifying
(4x + 6)(2x + -8) = 0

Reorder the terms:
(6 + 4x)(2x + -8) = 0

Reorder the terms:
(6 + 4x)(-8 + 2x) = 0

Multiply (6 + 4x) * (-8 + 2x)
(6(-8 + 2x) + 4x * (-8 + 2x)) = 0
((-8 * 6 + 2x * 6) + 4x * (-8 + 2x)) = 0
((-48 + 12x) + 4x * (-8 + 2x)) = 0
(-48 + 12x + (-8 * 4x + 2x * 4x)) = 0
(-48 + 12x + (-32x + 8x2)) = 0

Combine like terms: 12x + -32x = -20x
(-48 + -20x + 8x2) = 0

Solving
-48 + -20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -5x + 2x2) = 0

Factor a trinomial.
4((-3 + -2x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.5, 4}

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