2x(3x+4)=8

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Solution for 2x(3x+4)=8 equation: 


Simplifying
2x(3x + 4) = 8

Reorder the terms:
2x(4 + 3x) = 8
(4 * 2x + 3x * 2x) = 8
(8x + 6x2) = 8

Solving
8x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 8x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 4x + 3x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 0.6666666667}

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