(3x+1)(x-6)=0

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Solution for (3x+1)(x-6)=0 equation:


Simplifying
(3x + 1)(x + -6) = 0

Reorder the terms:
(1 + 3x)(x + -6) = 0

Reorder the terms:
(1 + 3x)(-6 + x) = 0

Multiply (1 + 3x) * (-6 + x)
(1(-6 + x) + 3x * (-6 + x)) = 0
((-6 * 1 + x * 1) + 3x * (-6 + x)) = 0
((-6 + 1x) + 3x * (-6 + x)) = 0
(-6 + 1x + (-6 * 3x + x * 3x)) = 0
(-6 + 1x + (-18x + 3x2)) = 0

Combine like terms: 1x + -18x = -17x
(-6 + -17x + 3x2) = 0

Solving
-6 + -17x + 3x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333

Subproblem 2

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

Solution

x = {-0.3333333333, 6}

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