5x^2=13x+6

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


Simplifying
5x2 = 13x + 6

Reorder the terms:
5x2 = 6 + 13x

Solving
5x2 = 6 + 13x

Solving for variable 'x'.

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

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

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

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

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

Subproblem 1

Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4

Subproblem 2

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

Solution

x = {-0.4, 3}

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