(x-1)(x-4)=(2x-5)(x-5)

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Solution for (x-1)(x-4)=(2x-5)(x-5) equation: 


Simplifying
(x + -1)(x + -4) = (2x + -5)(x + -5)

Reorder the terms:
(-1 + x)(x + -4) = (2x + -5)(x + -5)

Reorder the terms:
(-1 + x)(-4 + x) = (2x + -5)(x + -5)

Multiply (-1 + x) * (-4 + x)
(-1(-4 + x) + x(-4 + x)) = (2x + -5)(x + -5)
((-4 * -1 + x * -1) + x(-4 + x)) = (2x + -5)(x + -5)
((4 + -1x) + x(-4 + x)) = (2x + -5)(x + -5)
(4 + -1x + (-4 * x + x * x)) = (2x + -5)(x + -5)
(4 + -1x + (-4x + x2)) = (2x + -5)(x + -5)

Combine like terms: -1x + -4x = -5x
(4 + -5x + x2) = (2x + -5)(x + -5)

Reorder the terms:
4 + -5x + x2 = (-5 + 2x)(x + -5)

Reorder the terms:
4 + -5x + x2 = (-5 + 2x)(-5 + x)

Multiply (-5 + 2x) * (-5 + x)
4 + -5x + x2 = (-5(-5 + x) + 2x * (-5 + x))
4 + -5x + x2 = ((-5 * -5 + x * -5) + 2x * (-5 + x))
4 + -5x + x2 = ((25 + -5x) + 2x * (-5 + x))
4 + -5x + x2 = (25 + -5x + (-5 * 2x + x * 2x))
4 + -5x + x2 = (25 + -5x + (-10x + 2x2))

Combine like terms: -5x + -10x = -15x
4 + -5x + x2 = (25 + -15x + 2x2)

Solving
4 + -5x + x2 = 25 + -15x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + -25 + -5x + 15x + x2 + -2x2 = 25 + -15x + 2x2 + -25 + 15x + -2x2

Combine like terms: 4 + -25 = -21
-21 + -5x + 15x + x2 + -2x2 = 25 + -15x + 2x2 + -25 + 15x + -2x2

Combine like terms: -5x + 15x = 10x
-21 + 10x + x2 + -2x2 = 25 + -15x + 2x2 + -25 + 15x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-21 + 10x + -1x2 = 25 + -15x + 2x2 + -25 + 15x + -2x2

Reorder the terms:
-21 + 10x + -1x2 = 25 + -25 + -15x + 15x + 2x2 + -2x2

Combine like terms: 25 + -25 = 0
-21 + 10x + -1x2 = 0 + -15x + 15x + 2x2 + -2x2
-21 + 10x + -1x2 = -15x + 15x + 2x2 + -2x2

Combine like terms: -15x + 15x = 0
-21 + 10x + -1x2 = 0 + 2x2 + -2x2
-21 + 10x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-21 + 10x + -1x2 = 0

Factor a trinomial.
(-7 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

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 = {7, 3}

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