(x-6)(3x-2)=(2x-3)(x-10)

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Solution for (x-6)(3x-2)=(2x-3)(x-10) equation:


Simplifying
(x + -6)(3x + -2) = (2x + -3)(x + -10)

Reorder the terms:
(-6 + x)(3x + -2) = (2x + -3)(x + -10)

Reorder the terms:
(-6 + x)(-2 + 3x) = (2x + -3)(x + -10)

Multiply (-6 + x) * (-2 + 3x)
(-6(-2 + 3x) + x(-2 + 3x)) = (2x + -3)(x + -10)
((-2 * -6 + 3x * -6) + x(-2 + 3x)) = (2x + -3)(x + -10)
((12 + -18x) + x(-2 + 3x)) = (2x + -3)(x + -10)
(12 + -18x + (-2 * x + 3x * x)) = (2x + -3)(x + -10)
(12 + -18x + (-2x + 3x2)) = (2x + -3)(x + -10)

Combine like terms: -18x + -2x = -20x
(12 + -20x + 3x2) = (2x + -3)(x + -10)

Reorder the terms:
12 + -20x + 3x2 = (-3 + 2x)(x + -10)

Reorder the terms:
12 + -20x + 3x2 = (-3 + 2x)(-10 + x)

Multiply (-3 + 2x) * (-10 + x)
12 + -20x + 3x2 = (-3(-10 + x) + 2x * (-10 + x))
12 + -20x + 3x2 = ((-10 * -3 + x * -3) + 2x * (-10 + x))
12 + -20x + 3x2 = ((30 + -3x) + 2x * (-10 + x))
12 + -20x + 3x2 = (30 + -3x + (-10 * 2x + x * 2x))
12 + -20x + 3x2 = (30 + -3x + (-20x + 2x2))

Combine like terms: -3x + -20x = -23x
12 + -20x + 3x2 = (30 + -23x + 2x2)

Solving
12 + -20x + 3x2 = 30 + -23x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + -30 + -20x + 23x + 3x2 + -2x2 = 30 + -23x + 2x2 + -30 + 23x + -2x2

Combine like terms: 12 + -30 = -18
-18 + -20x + 23x + 3x2 + -2x2 = 30 + -23x + 2x2 + -30 + 23x + -2x2

Combine like terms: -20x + 23x = 3x
-18 + 3x + 3x2 + -2x2 = 30 + -23x + 2x2 + -30 + 23x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-18 + 3x + 1x2 = 30 + -23x + 2x2 + -30 + 23x + -2x2

Reorder the terms:
-18 + 3x + 1x2 = 30 + -30 + -23x + 23x + 2x2 + -2x2

Combine like terms: 30 + -30 = 0
-18 + 3x + 1x2 = 0 + -23x + 23x + 2x2 + -2x2
-18 + 3x + 1x2 = -23x + 23x + 2x2 + -2x2

Combine like terms: -23x + 23x = 0
-18 + 3x + 1x2 = 0 + 2x2 + -2x2
-18 + 3x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18 + 3x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-6, 3}

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