6x(4x+3)=6(-4x-3)

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


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

Reorder the terms:
6x(3 + 4x) = 6(-4x + -3)
(3 * 6x + 4x * 6x) = 6(-4x + -3)
(18x + 24x2) = 6(-4x + -3)

Reorder the terms:
18x + 24x2 = 6(-3 + -4x)
18x + 24x2 = (-3 * 6 + -4x * 6)
18x + 24x2 = (-18 + -24x)

Solving
18x + 24x2 = -18 + -24x

Solving for variable 'x'.

Reorder the terms:
18 + 18x + 24x + 24x2 = -18 + -24x + 18 + 24x

Combine like terms: 18x + 24x = 42x
18 + 42x + 24x2 = -18 + -24x + 18 + 24x

Reorder the terms:
18 + 42x + 24x2 = -18 + 18 + -24x + 24x

Combine like terms: -18 + 18 = 0
18 + 42x + 24x2 = 0 + -24x + 24x
18 + 42x + 24x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
18 + 42x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 7x + 4x2) = 0

Factor a trinomial.
6((1 + x)(3 + 4x)) = 0

Ignore the factor 6.

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 '(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
Solution
x = {-1, -0.75}

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