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

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


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

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

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

Multiply (-1 + x) * (2 + 3x)
(-1(2 + 3x) + x(2 + 3x)) = 4x
((2 * -1 + 3x * -1) + x(2 + 3x)) = 4x
((-2 + -3x) + x(2 + 3x)) = 4x
(-2 + -3x + (2 * x + 3x * x)) = 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.
(-1 + -3x)(2 + -1x) = 0


Subproblem 1
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

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 = {-0.3333333333, 2}

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