(3x+1)(x)=30

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Solution for (3x+1)(x)=30 equation:


Simplifying
(3x + 1)(x) = 30

Reorder the terms:
(1 + 3x)(x) = 30

Reorder the terms for easier multiplication:
x(1 + 3x) = 30
(1 * x + 3x * x) = 30
(1x + 3x2) = 30

Solving
1x + 3x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 1x + 3x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 1x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-10 + -3x)' equal to zero and attempt to solve: Simplifying -10 + -3x = 0 Solving -10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -3x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3x = 0 + 10 -3x = 0 + 10 Combine like terms: 0 + 10 = 10 -3x = 10 Divide each side by '-3'. x = -3.333333333 Simplifying x = -3.333333333

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 = {-3.333333333, 3}

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