x(x-5)=-6(x-2)

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Solution for x(x-5)=-6(x-2) equation: 


Simplifying
x(x + -5) = -6(x + -2)

Reorder the terms:
x(-5 + x) = -6(x + -2)
(-5 * x + x * x) = -6(x + -2)
(-5x + x2) = -6(x + -2)

Reorder the terms:
-5x + x2 = -6(-2 + x)
-5x + x2 = (-2 * -6 + x * -6)
-5x + x2 = (12 + -6x)

Solving
-5x + x2 = 12 + -6x

Solving for variable 'x'.

Reorder the terms:
-12 + -5x + 6x + x2 = 12 + -6x + -12 + 6x

Combine like terms: -5x + 6x = 1x
-12 + 1x + x2 = 12 + -6x + -12 + 6x

Reorder the terms:
-12 + 1x + x2 = 12 + -12 + -6x + 6x

Combine like terms: 12 + -12 = 0
-12 + 1x + x2 = 0 + -6x + 6x
-12 + 1x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-12 + 1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 3}

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