24x^2=-13x+2

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Solution for 24x^2=-13x+2 equation:


Simplifying
24x2 = -13x + 2

Reorder the terms:
24x2 = 2 + -13x

Solving
24x2 = 2 + -13x

Solving for variable 'x'.

Reorder the terms:
-2 + 13x + 24x2 = 2 + -13x + -2 + 13x

Reorder the terms:
-2 + 13x + 24x2 = 2 + -2 + -13x + 13x

Combine like terms: 2 + -2 = 0
-2 + 13x + 24x2 = 0 + -13x + 13x
-2 + 13x + 24x2 = -13x + 13x

Combine like terms: -13x + 13x = 0
-2 + 13x + 24x2 = 0

Factor a trinomial.
(-2 + -3x)(1 + -8x) = 0

Subproblem 1

Set the factor '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 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 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667

Subproblem 2

Set the factor '(1 + -8x)' equal to zero and attempt to solve: Simplifying 1 + -8x = 0 Solving 1 + -8x = 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 + -8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x = 0 + -1 -8x = 0 + -1 Combine like terms: 0 + -1 = -1 -8x = -1 Divide each side by '-8'. x = 0.125 Simplifying x = 0.125

Solution

x = {-0.6666666667, 0.125}

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