2x(x-2)=-3(x-2)

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Solution for 2x(x-2)=-3(x-2) equation: 


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

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

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

Solving
-4x + 2x2 = 6 + -3x

Solving for variable 'x'.

Reorder the terms:
-6 + -4x + 3x + 2x2 = 6 + -3x + -6 + 3x

Combine like terms: -4x + 3x = -1x
-6 + -1x + 2x2 = 6 + -3x + -6 + 3x

Reorder the terms:
-6 + -1x + 2x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
-6 + -1x + 2x2 = 0 + -3x + 3x
-6 + -1x + 2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-6 + -1x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(2 + -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 '(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 = {-1.5, 2}

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