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

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Solution for 133=(x+1)(3x+1) equation:


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

Reorder the terms:
133 = (1 + x)(3x + 1)

Reorder the terms:
133 = (1 + x)(1 + 3x)

Multiply (1 + x) * (1 + 3x)
133 = (1(1 + 3x) + x(1 + 3x))
133 = ((1 * 1 + 3x * 1) + x(1 + 3x))
133 = ((1 + 3x) + x(1 + 3x))
133 = (1 + 3x + (1 * x + 3x * x))
133 = (1 + 3x + (1x + 3x2))

Combine like terms: 3x + 1x = 4x
133 = (1 + 4x + 3x2)

Solving
133 = 1 + 4x + 3x2

Solving for variable 'x'.

Combine like terms: 133 + -1 = 132
132 + -4x + -3x2 = 1 + 4x + 3x2 + -1 + -4x + -3x2

Reorder the terms:
132 + -4x + -3x2 = 1 + -1 + 4x + -4x + 3x2 + -3x2

Combine like terms: 1 + -1 = 0
132 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2
132 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2

Combine like terms: 4x + -4x = 0
132 + -4x + -3x2 = 0 + 3x2 + -3x2
132 + -4x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
132 + -4x + -3x2 = 0

Factor a trinomial.
(6 + -1x)(22 + 3x) = 0

Subproblem 1

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Subproblem 2

Set the factor '(22 + 3x)' equal to zero and attempt to solve: Simplifying 22 + 3x = 0 Solving 22 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + 3x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 3x = 0 + -22 3x = 0 + -22 Combine like terms: 0 + -22 = -22 3x = -22 Divide each side by '3'. x = -7.333333333 Simplifying x = -7.333333333

Solution

x = {6, -7.333333333}

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