24x^2+42x-27=0

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Solution for 24x^2+42x-27=0 equation:


Simplifying
24x2 + 42x + -27 = 0

Reorder the terms:
-27 + 42x + 24x2 = 0

Solving
-27 + 42x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 14x + 8x2) = 0

Factor a trinomial.
3((-9 + -4x)(1 + -2x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-9 + -4x)' equal to zero and attempt to solve: Simplifying -9 + -4x = 0 Solving -9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x = 0 + 9 -4x = 0 + 9 Combine like terms: 0 + 9 = 9 -4x = 9 Divide each side by '-4'. x = -2.25 Simplifying x = -2.25

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-2.25, 0.5}

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