(x+5)(5x-4)=(x-4)(1-3x)

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Solution for (x+5)(5x-4)=(x-4)(1-3x) equation: 


Simplifying
(x + 5)(5x + -4) = (x + -4)(1 + -3x)

Reorder the terms:
(5 + x)(5x + -4) = (x + -4)(1 + -3x)

Reorder the terms:
(5 + x)(-4 + 5x) = (x + -4)(1 + -3x)

Multiply (5 + x) * (-4 + 5x)
(5(-4 + 5x) + x(-4 + 5x)) = (x + -4)(1 + -3x)
((-4 * 5 + 5x * 5) + x(-4 + 5x)) = (x + -4)(1 + -3x)
((-20 + 25x) + x(-4 + 5x)) = (x + -4)(1 + -3x)
(-20 + 25x + (-4 * x + 5x * x)) = (x + -4)(1 + -3x)
(-20 + 25x + (-4x + 5x2)) = (x + -4)(1 + -3x)

Combine like terms: 25x + -4x = 21x
(-20 + 21x + 5x2) = (x + -4)(1 + -3x)

Reorder the terms:
-20 + 21x + 5x2 = (-4 + x)(1 + -3x)

Multiply (-4 + x) * (1 + -3x)
-20 + 21x + 5x2 = (-4(1 + -3x) + x(1 + -3x))
-20 + 21x + 5x2 = ((1 * -4 + -3x * -4) + x(1 + -3x))
-20 + 21x + 5x2 = ((-4 + 12x) + x(1 + -3x))
-20 + 21x + 5x2 = (-4 + 12x + (1 * x + -3x * x))
-20 + 21x + 5x2 = (-4 + 12x + (1x + -3x2))

Combine like terms: 12x + 1x = 13x
-20 + 21x + 5x2 = (-4 + 13x + -3x2)

Solving
-20 + 21x + 5x2 = -4 + 13x + -3x2

Solving for variable 'x'.

Reorder the terms:
-20 + 4 + 21x + -13x + 5x2 + 3x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2

Combine like terms: -20 + 4 = -16
-16 + 21x + -13x + 5x2 + 3x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2

Combine like terms: 21x + -13x = 8x
-16 + 8x + 5x2 + 3x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2

Combine like terms: 5x2 + 3x2 = 8x2
-16 + 8x + 8x2 = -4 + 13x + -3x2 + 4 + -13x + 3x2

Reorder the terms:
-16 + 8x + 8x2 = -4 + 4 + 13x + -13x + -3x2 + 3x2

Combine like terms: -4 + 4 = 0
-16 + 8x + 8x2 = 0 + 13x + -13x + -3x2 + 3x2
-16 + 8x + 8x2 = 13x + -13x + -3x2 + 3x2

Combine like terms: 13x + -13x = 0
-16 + 8x + 8x2 = 0 + -3x2 + 3x2
-16 + 8x + 8x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-16 + 8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + x + x2) = 0

Factor a trinomial.
8((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 8.

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 '(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 = {-2, 1}

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