2x(3x+4)-x=5x+8

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Solution for 2x(3x+4)-x=5x+8 equation: 


Simplifying
2x(3x + 4) + -1x = 5x + 8

Reorder the terms:
2x(4 + 3x) + -1x = 5x + 8
(4 * 2x + 3x * 2x) + -1x = 5x + 8
(8x + 6x2) + -1x = 5x + 8

Reorder the terms:
8x + -1x + 6x2 = 5x + 8

Combine like terms: 8x + -1x = 7x
7x + 6x2 = 5x + 8

Reorder the terms:
7x + 6x2 = 8 + 5x

Solving
7x + 6x2 = 8 + 5x

Solving for variable 'x'.

Reorder the terms:
-8 + 7x + -5x + 6x2 = 8 + 5x + -8 + -5x

Combine like terms: 7x + -5x = 2x
-8 + 2x + 6x2 = 8 + 5x + -8 + -5x

Reorder the terms:
-8 + 2x + 6x2 = 8 + -8 + 5x + -5x

Combine like terms: 8 + -8 = 0
-8 + 2x + 6x2 = 0 + 5x + -5x
-8 + 2x + 6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-8 + 2x + 6x2 = 0

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

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.333333333, 1}

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