6x^2=5-13x

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


Simplifying
6x2 = 5 + -13x

Solving
6x2 = 5 + -13x

Solving for variable 'x'.

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

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

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

Combine like terms: -13x + 13x = 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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