0=(2-x)(3-2x)

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Solution for 0=(2-x)(3-2x) equation:


Simplifying
0 = (2 + -1x)(3 + -2x)

Multiply (2 + -1x) * (3 + -2x)
0 = (2(3 + -2x) + -1x * (3 + -2x))
0 = ((3 * 2 + -2x * 2) + -1x * (3 + -2x))
0 = ((6 + -4x) + -1x * (3 + -2x))
0 = (6 + -4x + (3 * -1x + -2x * -1x))
0 = (6 + -4x + (-3x + 2x2))

Combine like terms: -4x + -3x = -7x
0 = (6 + -7x + 2x2)

Solving
0 = 6 + -7x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 7x + -2x2 = 6 + -7x + 2x2 + -6 + 7x + -2x2

Reorder the terms:
-6 + 7x + -2x2 = 6 + -6 + -7x + 7x + 2x2 + -2x2

Combine like terms: 6 + -6 = 0
-6 + 7x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2
-6 + 7x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-6 + 7x + -2x2 = 0 + 2x2 + -2x2
-6 + 7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 7x + -2x2 = 0

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

Subproblem 1

Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Subproblem 2

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

Solution

x = {2, 1.5}

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