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

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


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

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

Reorder the terms for easier multiplication:
-8x(3 + 6x) + -8(6x + 3) = 0
(3 * -8x + 6x * -8x) + -8(6x + 3) = 0
(-24x + -48x2) + -8(6x + 3) = 0

Reorder the terms:
-24x + -48x2 + -8(3 + 6x) = 0
-24x + -48x2 + (3 * -8 + 6x * -8) = 0
-24x + -48x2 + (-24 + -48x) = 0

Reorder the terms:
-24 + -24x + -48x + -48x2 = 0

Combine like terms: -24x + -48x = -72x
-24 + -72x + -48x2 = 0

Solving
-24 + -72x + -48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-24'.
-24(1 + 3x + 2x2) = 0

Factor a trinomial.
-24((1 + x)(1 + 2x)) = 0

Ignore the factor -24.

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

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 = {-1, -0.5}

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