(X+1)(5X+1)=(X+2)(X+3)

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Solution for (X+1)(5X+1)=(X+2)(X+3) equation:


Simplifying
(X + 1)(5X + 1) = (X + 2)(X + 3)

Reorder the terms:
(1 + X)(5X + 1) = (X + 2)(X + 3)

Reorder the terms:
(1 + X)(1 + 5X) = (X + 2)(X + 3)

Multiply (1 + X) * (1 + 5X)
(1(1 + 5X) + X(1 + 5X)) = (X + 2)(X + 3)
((1 * 1 + 5X * 1) + X(1 + 5X)) = (X + 2)(X + 3)
((1 + 5X) + X(1 + 5X)) = (X + 2)(X + 3)
(1 + 5X + (1 * X + 5X * X)) = (X + 2)(X + 3)
(1 + 5X + (1X + 5X2)) = (X + 2)(X + 3)

Combine like terms: 5X + 1X = 6X
(1 + 6X + 5X2) = (X + 2)(X + 3)

Reorder the terms:
1 + 6X + 5X2 = (2 + X)(X + 3)

Reorder the terms:
1 + 6X + 5X2 = (2 + X)(3 + X)

Multiply (2 + X) * (3 + X)
1 + 6X + 5X2 = (2(3 + X) + X(3 + X))
1 + 6X + 5X2 = ((3 * 2 + X * 2) + X(3 + X))
1 + 6X + 5X2 = ((6 + 2X) + X(3 + X))
1 + 6X + 5X2 = (6 + 2X + (3 * X + X * X))
1 + 6X + 5X2 = (6 + 2X + (3X + X2))

Combine like terms: 2X + 3X = 5X
1 + 6X + 5X2 = (6 + 5X + X2)

Solving
1 + 6X + 5X2 = 6 + 5X + X2

Solving for variable 'X'.

Reorder the terms:
1 + -6 + 6X + -5X + 5X2 + -1X2 = 6 + 5X + X2 + -6 + -5X + -1X2

Combine like terms: 1 + -6 = -5
-5 + 6X + -5X + 5X2 + -1X2 = 6 + 5X + X2 + -6 + -5X + -1X2

Combine like terms: 6X + -5X = 1X
-5 + 1X + 5X2 + -1X2 = 6 + 5X + X2 + -6 + -5X + -1X2

Combine like terms: 5X2 + -1X2 = 4X2
-5 + 1X + 4X2 = 6 + 5X + X2 + -6 + -5X + -1X2

Reorder the terms:
-5 + 1X + 4X2 = 6 + -6 + 5X + -5X + X2 + -1X2

Combine like terms: 6 + -6 = 0
-5 + 1X + 4X2 = 0 + 5X + -5X + X2 + -1X2
-5 + 1X + 4X2 = 5X + -5X + X2 + -1X2

Combine like terms: 5X + -5X = 0
-5 + 1X + 4X2 = 0 + X2 + -1X2
-5 + 1X + 4X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-5 + 1X + 4X2 = 0

Factor a trinomial.
(-5 + -4X)(1 + -1X) = 0

Subproblem 1

Set the factor '(-5 + -4X)' equal to zero and attempt to solve: Simplifying -5 + -4X = 0 Solving -5 + -4X = 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 + -4X = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4X = 0 + 5 -4X = 0 + 5 Combine like terms: 0 + 5 = 5 -4X = 5 Divide each side by '-4'. X = -1.25 Simplifying X = -1.25

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 = {-1.25, 1}

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