(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.
(-3 + -1x)(10 + -3x) = 0

Subproblem 1

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

Subproblem 2

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

Solution

x = {-3, 3.333333333}

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