(6x-3)*(4x+16)=0

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Solution for (6x-3)*(4x+16)=0 equation: 


Simplifying
(6x + -3)(4x + 16) = 0

Reorder the terms:
(-3 + 6x)(4x + 16) = 0

Reorder the terms:
(-3 + 6x)(16 + 4x) = 0

Multiply (-3 + 6x) * (16 + 4x)
(-3(16 + 4x) + 6x * (16 + 4x)) = 0
((16 * -3 + 4x * -3) + 6x * (16 + 4x)) = 0
((-48 + -12x) + 6x * (16 + 4x)) = 0
(-48 + -12x + (16 * 6x + 4x * 6x)) = 0
(-48 + -12x + (96x + 24x2)) = 0

Combine like terms: -12x + 96x = 84x
(-48 + 84x + 24x2) = 0

Solving
-48 + 84x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-4 + 7x + 2x2) = 0

Factor a trinomial.
12((-4 + -1x)(1 + -2x)) = 0

Ignore the factor 12.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 0.5}

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