(5x-4)(x-7)=(1-4x)(x+1)

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Solution for (5x-4)(x-7)=(1-4x)(x+1) equation: 


Simplifying
(5x + -4)(x + -7) = (1 + -4x)(x + 1)

Reorder the terms:
(-4 + 5x)(x + -7) = (1 + -4x)(x + 1)

Reorder the terms:
(-4 + 5x)(-7 + x) = (1 + -4x)(x + 1)

Multiply (-4 + 5x) * (-7 + x)
(-4(-7 + x) + 5x * (-7 + x)) = (1 + -4x)(x + 1)
((-7 * -4 + x * -4) + 5x * (-7 + x)) = (1 + -4x)(x + 1)
((28 + -4x) + 5x * (-7 + x)) = (1 + -4x)(x + 1)
(28 + -4x + (-7 * 5x + x * 5x)) = (1 + -4x)(x + 1)
(28 + -4x + (-35x + 5x2)) = (1 + -4x)(x + 1)

Combine like terms: -4x + -35x = -39x
(28 + -39x + 5x2) = (1 + -4x)(x + 1)

Reorder the terms:
28 + -39x + 5x2 = (1 + -4x)(1 + x)

Multiply (1 + -4x) * (1 + x)
28 + -39x + 5x2 = (1(1 + x) + -4x * (1 + x))
28 + -39x + 5x2 = ((1 * 1 + x * 1) + -4x * (1 + x))
28 + -39x + 5x2 = ((1 + 1x) + -4x * (1 + x))
28 + -39x + 5x2 = (1 + 1x + (1 * -4x + x * -4x))
28 + -39x + 5x2 = (1 + 1x + (-4x + -4x2))

Combine like terms: 1x + -4x = -3x
28 + -39x + 5x2 = (1 + -3x + -4x2)

Solving
28 + -39x + 5x2 = 1 + -3x + -4x2

Solving for variable 'x'.

Reorder the terms:
28 + -1 + -39x + 3x + 5x2 + 4x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2

Combine like terms: 28 + -1 = 27
27 + -39x + 3x + 5x2 + 4x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2

Combine like terms: -39x + 3x = -36x
27 + -36x + 5x2 + 4x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2

Combine like terms: 5x2 + 4x2 = 9x2
27 + -36x + 9x2 = 1 + -3x + -4x2 + -1 + 3x + 4x2

Reorder the terms:
27 + -36x + 9x2 = 1 + -1 + -3x + 3x + -4x2 + 4x2

Combine like terms: 1 + -1 = 0
27 + -36x + 9x2 = 0 + -3x + 3x + -4x2 + 4x2
27 + -36x + 9x2 = -3x + 3x + -4x2 + 4x2

Combine like terms: -3x + 3x = 0
27 + -36x + 9x2 = 0 + -4x2 + 4x2
27 + -36x + 9x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
27 + -36x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(3 + -4x + x2) = 0

Factor a trinomial.
9((1 + -1x)(3 + -1x)) = 0

Ignore the factor 9.

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 '(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 = {1, 3}

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