(3x+1)(x+1)=1

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Solution for (3x+1)(x+1)=1 equation:


Simplifying
(3x + 1)(x + 1) = 1

Reorder the terms:
(1 + 3x)(x + 1) = 1

Reorder the terms:
(1 + 3x)(1 + x) = 1

Multiply (1 + 3x) * (1 + x)
(1(1 + x) + 3x * (1 + x)) = 1
((1 * 1 + x * 1) + 3x * (1 + x)) = 1
((1 + 1x) + 3x * (1 + x)) = 1
(1 + 1x + (1 * 3x + x * 3x)) = 1
(1 + 1x + (3x + 3x2)) = 1

Combine like terms: 1x + 3x = 4x
(1 + 4x + 3x2) = 1

Add '-1' to each side of the equation.
1 + 4x + -1 + 3x2 = 1 + -1

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

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

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

Solving
4x + 3x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333

Solution

x = {0, -1.333333333}

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