24x^2=-10x+4

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Solution for 24x^2=-10x+4 equation: 


Simplifying
24x2 = -10x + 4

Reorder the terms:
24x2 = 4 + -10x

Solving
24x2 = 4 + -10x

Solving for variable 'x'.

Reorder the terms:
-4 + 10x + 24x2 = 4 + -10x + -4 + 10x

Reorder the terms:
-4 + 10x + 24x2 = 4 + -4 + -10x + 10x

Combine like terms: 4 + -4 = 0
-4 + 10x + 24x2 = 0 + -10x + 10x
-4 + 10x + 24x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-4 + 10x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5x + 12x2) = 0

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

Ignore the factor 2.

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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-0.6666666667, 0.25}

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