(9x-3)(4-x)=(9x-3)(-3x+2)

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Solution for (9x-3)(4-x)=(9x-3)(-3x+2) equation:


Simplifying
(9x + -3)(4 + -1x) = (9x + -3)(-3x + 2)

Reorder the terms:
(-3 + 9x)(4 + -1x) = (9x + -3)(-3x + 2)

Multiply (-3 + 9x) * (4 + -1x)
(-3(4 + -1x) + 9x * (4 + -1x)) = (9x + -3)(-3x + 2)
((4 * -3 + -1x * -3) + 9x * (4 + -1x)) = (9x + -3)(-3x + 2)
((-12 + 3x) + 9x * (4 + -1x)) = (9x + -3)(-3x + 2)
(-12 + 3x + (4 * 9x + -1x * 9x)) = (9x + -3)(-3x + 2)
(-12 + 3x + (36x + -9x2)) = (9x + -3)(-3x + 2)

Combine like terms: 3x + 36x = 39x
(-12 + 39x + -9x2) = (9x + -3)(-3x + 2)

Reorder the terms:
-12 + 39x + -9x2 = (-3 + 9x)(-3x + 2)

Reorder the terms:
-12 + 39x + -9x2 = (-3 + 9x)(2 + -3x)

Multiply (-3 + 9x) * (2 + -3x)
-12 + 39x + -9x2 = (-3(2 + -3x) + 9x * (2 + -3x))
-12 + 39x + -9x2 = ((2 * -3 + -3x * -3) + 9x * (2 + -3x))
-12 + 39x + -9x2 = ((-6 + 9x) + 9x * (2 + -3x))
-12 + 39x + -9x2 = (-6 + 9x + (2 * 9x + -3x * 9x))
-12 + 39x + -9x2 = (-6 + 9x + (18x + -27x2))

Combine like terms: 9x + 18x = 27x
-12 + 39x + -9x2 = (-6 + 27x + -27x2)

Solving
-12 + 39x + -9x2 = -6 + 27x + -27x2

Solving for variable 'x'.

Reorder the terms:
-12 + 6 + 39x + -27x + -9x2 + 27x2 = -6 + 27x + -27x2 + 6 + -27x + 27x2

Combine like terms: -12 + 6 = -6
-6 + 39x + -27x + -9x2 + 27x2 = -6 + 27x + -27x2 + 6 + -27x + 27x2

Combine like terms: 39x + -27x = 12x
-6 + 12x + -9x2 + 27x2 = -6 + 27x + -27x2 + 6 + -27x + 27x2

Combine like terms: -9x2 + 27x2 = 18x2
-6 + 12x + 18x2 = -6 + 27x + -27x2 + 6 + -27x + 27x2

Reorder the terms:
-6 + 12x + 18x2 = -6 + 6 + 27x + -27x + -27x2 + 27x2

Combine like terms: -6 + 6 = 0
-6 + 12x + 18x2 = 0 + 27x + -27x + -27x2 + 27x2
-6 + 12x + 18x2 = 27x + -27x + -27x2 + 27x2

Combine like terms: 27x + -27x = 0
-6 + 12x + 18x2 = 0 + -27x2 + 27x2
-6 + 12x + 18x2 = -27x2 + 27x2

Combine like terms: -27x2 + 27x2 = 0
-6 + 12x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 2x + 3x2) = 0

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

Ignore the factor 6.

Subproblem 1

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

Subproblem 2

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

Solution

x = {-1, 0.3333333333}

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