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

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


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

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

Reorder the terms:
-2x + 2x2 = 3(4 + x)
-2x + 2x2 = (4 * 3 + x * 3)
-2x + 2x2 = (12 + 3x)

Solving
-2x + 2x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + -2x + -3x + 2x2 = 12 + 3x + -12 + -3x

Combine like terms: -2x + -3x = -5x
-12 + -5x + 2x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-12 + -5x + 2x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-12 + -5x + 2x2 = 0 + 3x + -3x
-12 + -5x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 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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