x(2x+1)=6(x+2)

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Solution for x(2x+1)=6(x+2) equation: 


Simplifying
x(2x + 1) = 6(x + 2)

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

Reorder the terms:
1x + 2x2 = 6(2 + x)
1x + 2x2 = (2 * 6 + x * 6)
1x + 2x2 = (12 + 6x)

Solving
1x + 2x2 = 12 + 6x

Solving for variable 'x'.

Reorder the terms:
-12 + 1x + -6x + 2x2 = 12 + 6x + -12 + -6x

Combine like terms: 1x + -6x = -5x
-12 + -5x + 2x2 = 12 + 6x + -12 + -6x

Reorder the terms:
-12 + -5x + 2x2 = 12 + -12 + 6x + -6x

Combine like terms: 12 + -12 = 0
-12 + -5x + 2x2 = 0 + 6x + -6x
-12 + -5x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-12 + -5x + 2x2 = 0

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


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.5, 4}

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