0=6x^2+45x-24

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Solution for 0=6x^2+45x-24 equation:


Simplifying
0 = 6x2 + 45x + -24

Reorder the terms:
0 = -24 + 45x + 6x2

Solving
0 = -24 + 45x + 6x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {0.5, -8}

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