(1-x)(3x+2)=-4x

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Solution for (1-x)(3x+2)=-4x equation: 


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

Reorder the terms:
(1 + -1x)(2 + 3x) = -4x

Multiply (1 + -1x) * (2 + 3x)
(1(2 + 3x) + -1x * (2 + 3x)) = -4x
((2 * 1 + 3x * 1) + -1x * (2 + 3x)) = -4x
((2 + 3x) + -1x * (2 + 3x)) = -4x
(2 + 3x + (2 * -1x + 3x * -1x)) = -4x
(2 + 3x + (-2x + -3x2)) = -4x

Combine like terms: 3x + -2x = 1x
(2 + 1x + -3x2) = -4x

Solving
2 + 1x + -3x2 = -4x

Solving for variable 'x'.

Reorder the terms:
2 + 1x + 4x + -3x2 = -4x + 4x

Combine like terms: 1x + 4x = 5x
2 + 5x + -3x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
2 + 5x + -3x2 = 0

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


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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {2, -0.3333333333}

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