2x(3x+1)=28

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Solution for 2x(3x+1)=28 equation: 


Simplifying
2x(3x + 1) = 28

Reorder the terms:
2x(1 + 3x) = 28
(1 * 2x + 3x * 2x) = 28
(2x + 6x2) = 28

Solving
2x + 6x2 = 28

Solving for variable 'x'.

Reorder the terms:
-28 + 2x + 6x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + x + 3x2) = 0

Factor a trinomial.
2((-7 + -3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
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
Solution
x = {-2.333333333, 2}

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