-6x^2+13x=-5

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Solution for -6x^2+13x=-5 equation:


Simplifying
-6x2 + 13x = -5

Reorder the terms:
13x + -6x2 = -5

Solving
13x + -6x2 = -5

Solving for variable 'x'.

Reorder the terms:
5 + 13x + -6x2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 13x + -6x2 = 0

Factor a trinomial.
(5 + -2x)(1 + 3x) = 0

Subproblem 1

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Subproblem 2

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

Solution

x = {2.5, -0.3333333333}

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