(3x+1)(x+1)-40=0

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Solution for (3x+1)(x+1)-40=0 equation:


Simplifying
(3x + 1)(x + 1) + -40 = 0

Reorder the terms:
(1 + 3x)(x + 1) + -40 = 0

Reorder the terms:
(1 + 3x)(1 + x) + -40 = 0

Multiply (1 + 3x) * (1 + x)
(1(1 + x) + 3x * (1 + x)) + -40 = 0
((1 * 1 + x * 1) + 3x * (1 + x)) + -40 = 0
((1 + 1x) + 3x * (1 + x)) + -40 = 0
(1 + 1x + (1 * 3x + x * 3x)) + -40 = 0
(1 + 1x + (3x + 3x2)) + -40 = 0

Combine like terms: 1x + 3x = 4x
(1 + 4x + 3x2) + -40 = 0

Reorder the terms:
1 + -40 + 4x + 3x2 = 0

Combine like terms: 1 + -40 = -39
-39 + 4x + 3x2 = 0

Solving
-39 + 4x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + -3x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-13 + -3x)' equal to zero and attempt to solve: Simplifying -13 + -3x = 0 Solving -13 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -3x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3x = 0 + 13 -3x = 0 + 13 Combine like terms: 0 + 13 = 13 -3x = 13 Divide each side by '-3'. x = -4.333333333 Simplifying x = -4.333333333

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-4.333333333, 3}

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