6x^2+29x=65

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Solution for 6x^2+29x=65 equation:


Simplifying
6x2 + 29x = 65

Reorder the terms:
29x + 6x2 = 65

Solving
29x + 6x2 = 65

Solving for variable 'x'.

Reorder the terms:
-65 + 29x + 6x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-65 + 29x + 6x2 = 0

Factor a trinomial.
(-13 + -2x)(5 + -3x) = 0

Subproblem 1

Set the factor '(-13 + -2x)' equal to zero and attempt to solve: Simplifying -13 + -2x = 0 Solving -13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x = 0 + 13 -2x = 0 + 13 Combine like terms: 0 + 13 = 13 -2x = 13 Divide each side by '-2'. x = -6.5 Simplifying x = -6.5

Subproblem 2

Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {-6.5, 1.666666667}

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