6(x-3)-20x=x(x-3)

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Solution for 6(x-3)-20x=x(x-3) equation:


Simplifying
6(x + -3) + -20x = x(x + -3)

Reorder the terms:
6(-3 + x) + -20x = x(x + -3)
(-3 * 6 + x * 6) + -20x = x(x + -3)
(-18 + 6x) + -20x = x(x + -3)

Combine like terms: 6x + -20x = -14x
-18 + -14x = x(x + -3)

Reorder the terms:
-18 + -14x = x(-3 + x)
-18 + -14x = (-3 * x + x * x)
-18 + -14x = (-3x + x2)

Solving
-18 + -14x = -3x + x2

Solving for variable 'x'.

Combine like terms: -14x + 3x = -11x
-18 + -11x + -1x2 = -3x + x2 + 3x + -1x2

Reorder the terms:
-18 + -11x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-18 + -11x + -1x2 = 0 + x2 + -1x2
-18 + -11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -11x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 11x + x2) = 0

Factor a trinomial.
-1((9 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9

Subproblem 2

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

Solution

x = {-9, -2}

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