(3x-1)(x)=310

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Solution for (3x-1)(x)=310 equation:


Simplifying
(3x + -1)(x) = 310

Reorder the terms:
(-1 + 3x)(x) = 310

Reorder the terms for easier multiplication:
x(-1 + 3x) = 310
(-1 * x + 3x * x) = 310
(-1x + 3x2) = 310

Solving
-1x + 3x2 = 310

Solving for variable 'x'.

Reorder the terms:
-310 + -1x + 3x2 = 310 + -310

Combine like terms: 310 + -310 = 0
-310 + -1x + 3x2 = 0

Factor a trinomial.
(-10 + -1x)(31 + -3x) = 0

Subproblem 1

Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 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 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10

Subproblem 2

Set the factor '(31 + -3x)' equal to zero and attempt to solve: Simplifying 31 + -3x = 0 Solving 31 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -3x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -3x = 0 + -31 -3x = 0 + -31 Combine like terms: 0 + -31 = -31 -3x = -31 Divide each side by '-3'. x = 10.33333333 Simplifying x = 10.33333333

Solution

x = {-10, 10.33333333}

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