(X+1)(X+3)=6X+11

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Solution for (X+1)(X+3)=6X+11 equation:


Simplifying
(X + 1)(X + 3) = 6X + 11

Reorder the terms:
(1 + X)(X + 3) = 6X + 11

Reorder the terms:
(1 + X)(3 + X) = 6X + 11

Multiply (1 + X) * (3 + X)
(1(3 + X) + X(3 + X)) = 6X + 11
((3 * 1 + X * 1) + X(3 + X)) = 6X + 11
((3 + 1X) + X(3 + X)) = 6X + 11
(3 + 1X + (3 * X + X * X)) = 6X + 11
(3 + 1X + (3X + X2)) = 6X + 11

Combine like terms: 1X + 3X = 4X
(3 + 4X + X2) = 6X + 11

Reorder the terms:
3 + 4X + X2 = 11 + 6X

Solving
3 + 4X + X2 = 11 + 6X

Solving for variable 'X'.

Reorder the terms:
3 + -11 + 4X + -6X + X2 = 11 + 6X + -11 + -6X

Combine like terms: 3 + -11 = -8
-8 + 4X + -6X + X2 = 11 + 6X + -11 + -6X

Combine like terms: 4X + -6X = -2X
-8 + -2X + X2 = 11 + 6X + -11 + -6X

Reorder the terms:
-8 + -2X + X2 = 11 + -11 + 6X + -6X

Combine like terms: 11 + -11 = 0
-8 + -2X + X2 = 0 + 6X + -6X
-8 + -2X + X2 = 6X + -6X

Combine like terms: 6X + -6X = 0
-8 + -2X + X2 = 0

Factor a trinomial.
(-2 + -1X)(4 + -1X) = 0

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 '(4 + -1X)' equal to zero and attempt to solve: Simplifying 4 + -1X = 0 Solving 4 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1X = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1X = 0 + -4 -1X = 0 + -4 Combine like terms: 0 + -4 = -4 -1X = -4 Divide each side by '-1'. X = 4 Simplifying X = 4

Solution

X = {-2, 4}

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