(2x-5)(x-4)-7=(x-2)(x-3)

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Solution for (2x-5)(x-4)-7=(x-2)(x-3) equation: 


Simplifying
(2x + -5)(x + -4) + -7 = (x + -2)(x + -3)

Reorder the terms:
(-5 + 2x)(x + -4) + -7 = (x + -2)(x + -3)

Reorder the terms:
(-5 + 2x)(-4 + x) + -7 = (x + -2)(x + -3)

Multiply (-5 + 2x) * (-4 + x)
(-5(-4 + x) + 2x * (-4 + x)) + -7 = (x + -2)(x + -3)
((-4 * -5 + x * -5) + 2x * (-4 + x)) + -7 = (x + -2)(x + -3)
((20 + -5x) + 2x * (-4 + x)) + -7 = (x + -2)(x + -3)
(20 + -5x + (-4 * 2x + x * 2x)) + -7 = (x + -2)(x + -3)
(20 + -5x + (-8x + 2x2)) + -7 = (x + -2)(x + -3)

Combine like terms: -5x + -8x = -13x
(20 + -13x + 2x2) + -7 = (x + -2)(x + -3)

Reorder the terms:
20 + -7 + -13x + 2x2 = (x + -2)(x + -3)

Combine like terms: 20 + -7 = 13
13 + -13x + 2x2 = (x + -2)(x + -3)

Reorder the terms:
13 + -13x + 2x2 = (-2 + x)(x + -3)

Reorder the terms:
13 + -13x + 2x2 = (-2 + x)(-3 + x)

Multiply (-2 + x) * (-3 + x)
13 + -13x + 2x2 = (-2(-3 + x) + x(-3 + x))
13 + -13x + 2x2 = ((-3 * -2 + x * -2) + x(-3 + x))
13 + -13x + 2x2 = ((6 + -2x) + x(-3 + x))
13 + -13x + 2x2 = (6 + -2x + (-3 * x + x * x))
13 + -13x + 2x2 = (6 + -2x + (-3x + x2))

Combine like terms: -2x + -3x = -5x
13 + -13x + 2x2 = (6 + -5x + x2)

Solving
13 + -13x + 2x2 = 6 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
13 + -6 + -13x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: 13 + -6 = 7
7 + -13x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: -13x + 5x = -8x
7 + -8x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
7 + -8x + 1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Reorder the terms:
7 + -8x + 1x2 = 6 + -6 + -5x + 5x + x2 + -1x2

Combine like terms: 6 + -6 = 0
7 + -8x + 1x2 = 0 + -5x + 5x + x2 + -1x2
7 + -8x + 1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
7 + -8x + 1x2 = 0 + x2 + -1x2
7 + -8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + -8x + 1x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}

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