(2x-7)(x-4)=(4x-19)(x-2)

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Solution for (2x-7)(x-4)=(4x-19)(x-2) equation: 


Simplifying
(2x + -7)(x + -4) = (4x + -19)(x + -2)

Reorder the terms:
(-7 + 2x)(x + -4) = (4x + -19)(x + -2)

Reorder the terms:
(-7 + 2x)(-4 + x) = (4x + -19)(x + -2)

Multiply (-7 + 2x) * (-4 + x)
(-7(-4 + x) + 2x * (-4 + x)) = (4x + -19)(x + -2)
((-4 * -7 + x * -7) + 2x * (-4 + x)) = (4x + -19)(x + -2)
((28 + -7x) + 2x * (-4 + x)) = (4x + -19)(x + -2)
(28 + -7x + (-4 * 2x + x * 2x)) = (4x + -19)(x + -2)
(28 + -7x + (-8x + 2x2)) = (4x + -19)(x + -2)

Combine like terms: -7x + -8x = -15x
(28 + -15x + 2x2) = (4x + -19)(x + -2)

Reorder the terms:
28 + -15x + 2x2 = (-19 + 4x)(x + -2)

Reorder the terms:
28 + -15x + 2x2 = (-19 + 4x)(-2 + x)

Multiply (-19 + 4x) * (-2 + x)
28 + -15x + 2x2 = (-19(-2 + x) + 4x * (-2 + x))
28 + -15x + 2x2 = ((-2 * -19 + x * -19) + 4x * (-2 + x))
28 + -15x + 2x2 = ((38 + -19x) + 4x * (-2 + x))
28 + -15x + 2x2 = (38 + -19x + (-2 * 4x + x * 4x))
28 + -15x + 2x2 = (38 + -19x + (-8x + 4x2))

Combine like terms: -19x + -8x = -27x
28 + -15x + 2x2 = (38 + -27x + 4x2)

Solving
28 + -15x + 2x2 = 38 + -27x + 4x2

Solving for variable 'x'.

Reorder the terms:
28 + -38 + -15x + 27x + 2x2 + -4x2 = 38 + -27x + 4x2 + -38 + 27x + -4x2

Combine like terms: 28 + -38 = -10
-10 + -15x + 27x + 2x2 + -4x2 = 38 + -27x + 4x2 + -38 + 27x + -4x2

Combine like terms: -15x + 27x = 12x
-10 + 12x + 2x2 + -4x2 = 38 + -27x + 4x2 + -38 + 27x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-10 + 12x + -2x2 = 38 + -27x + 4x2 + -38 + 27x + -4x2

Reorder the terms:
-10 + 12x + -2x2 = 38 + -38 + -27x + 27x + 4x2 + -4x2

Combine like terms: 38 + -38 = 0
-10 + 12x + -2x2 = 0 + -27x + 27x + 4x2 + -4x2
-10 + 12x + -2x2 = -27x + 27x + 4x2 + -4x2

Combine like terms: -27x + 27x = 0
-10 + 12x + -2x2 = 0 + 4x2 + -4x2
-10 + 12x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-10 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6x + -1x2) = 0

Factor a trinomial.
2((-5 + x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

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

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, 1}

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