x(x-3)-30=5(x-2)

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Solution for x(x-3)-30=5(x-2) equation: 


Simplifying
x(x + -3) + -30 = 5(x + -2)

Reorder the terms:
x(-3 + x) + -30 = 5(x + -2)
(-3 * x + x * x) + -30 = 5(x + -2)
(-3x + x2) + -30 = 5(x + -2)

Reorder the terms:
-30 + -3x + x2 = 5(x + -2)

Reorder the terms:
-30 + -3x + x2 = 5(-2 + x)
-30 + -3x + x2 = (-2 * 5 + x * 5)
-30 + -3x + x2 = (-10 + 5x)

Solving
-30 + -3x + x2 = -10 + 5x

Solving for variable 'x'.

Reorder the terms:
-30 + 10 + -3x + -5x + x2 = -10 + 5x + 10 + -5x

Combine like terms: -30 + 10 = -20
-20 + -3x + -5x + x2 = -10 + 5x + 10 + -5x

Combine like terms: -3x + -5x = -8x
-20 + -8x + x2 = -10 + 5x + 10 + -5x

Reorder the terms:
-20 + -8x + x2 = -10 + 10 + 5x + -5x

Combine like terms: -10 + 10 = 0
-20 + -8x + x2 = 0 + 5x + -5x
-20 + -8x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-20 + -8x + x2 = 0

Factor a trinomial.
(-2 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-2, 10}

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