x(x-3)-4x=5(x-4)

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Solution for x(x-3)-4x=5(x-4) equation: 


Simplifying
x(x + -3) + -4x = 5(x + -4)

Reorder the terms:
x(-3 + x) + -4x = 5(x + -4)
(-3 * x + x * x) + -4x = 5(x + -4)
(-3x + x2) + -4x = 5(x + -4)

Reorder the terms:
-3x + -4x + x2 = 5(x + -4)

Combine like terms: -3x + -4x = -7x
-7x + x2 = 5(x + -4)

Reorder the terms:
-7x + x2 = 5(-4 + x)
-7x + x2 = (-4 * 5 + x * 5)
-7x + x2 = (-20 + 5x)

Solving
-7x + x2 = -20 + 5x

Solving for variable 'x'.

Reorder the terms:
20 + -7x + -5x + x2 = -20 + 5x + 20 + -5x

Combine like terms: -7x + -5x = -12x
20 + -12x + x2 = -20 + 5x + 20 + -5x

Reorder the terms:
20 + -12x + x2 = -20 + 20 + 5x + -5x

Combine like terms: -20 + 20 = 0
20 + -12x + x2 = 0 + 5x + -5x
20 + -12x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
20 + -12x + 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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