.5x(6x+4)=x+2(x+1)

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Solution for .5x(6x+4)=x+2(x+1) equation: 


Simplifying
0.5x(6x + 4) = x + 2(x + 1)

Reorder the terms:
0.5x(4 + 6x) = x + 2(x + 1)
(4 * 0.5x + 6x * 0.5x) = x + 2(x + 1)
(2x + 3x2) = x + 2(x + 1)

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

Reorder the terms:
2x + 3x2 = 2 + x + 2x

Combine like terms: x + 2x = 3x
2x + 3x2 = 2 + 3x

Solving
2x + 3x2 = 2 + 3x

Solving for variable 'x'.

Reorder the terms:
-2 + 2x + -3x + 3x2 = 2 + 3x + -2 + -3x

Combine like terms: 2x + -3x = -1x
-2 + -1x + 3x2 = 2 + 3x + -2 + -3x

Reorder the terms:
-2 + -1x + 3x2 = 2 + -2 + 3x + -3x

Combine like terms: 2 + -2 = 0
-2 + -1x + 3x2 = 0 + 3x + -3x
-2 + -1x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-2 + -1x + 3x2 = 0

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


Subproblem 1
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

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 = {-0.6666666667, 1}

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