24x^2-6x=45

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Solution for 24x^2-6x=45 equation:


Simplifying
24x2 + -6x = 45

Reorder the terms:
-6x + 24x2 = 45

Solving
-6x + 24x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + -6x + 24x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -6x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2x + 8x2) = 0

Factor a trinomial.
3((-5 + -4x)(3 + -2x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-1.25, 1.5}

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