(24x-16)(6x-14)=480x-320

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Solution for (24x-16)(6x-14)=480x-320 equation: 


Simplifying
(24x + -16)(6x + -14) = 480x + -320

Reorder the terms:
(-16 + 24x)(6x + -14) = 480x + -320

Reorder the terms:
(-16 + 24x)(-14 + 6x) = 480x + -320

Multiply (-16 + 24x) * (-14 + 6x)
(-16(-14 + 6x) + 24x * (-14 + 6x)) = 480x + -320
((-14 * -16 + 6x * -16) + 24x * (-14 + 6x)) = 480x + -320
((224 + -96x) + 24x * (-14 + 6x)) = 480x + -320
(224 + -96x + (-14 * 24x + 6x * 24x)) = 480x + -320
(224 + -96x + (-336x + 144x2)) = 480x + -320

Combine like terms: -96x + -336x = -432x
(224 + -432x + 144x2) = 480x + -320

Reorder the terms:
224 + -432x + 144x2 = -320 + 480x

Solving
224 + -432x + 144x2 = -320 + 480x

Solving for variable 'x'.

Reorder the terms:
224 + 320 + -432x + -480x + 144x2 = -320 + 480x + 320 + -480x

Combine like terms: 224 + 320 = 544
544 + -432x + -480x + 144x2 = -320 + 480x + 320 + -480x

Combine like terms: -432x + -480x = -912x
544 + -912x + 144x2 = -320 + 480x + 320 + -480x

Reorder the terms:
544 + -912x + 144x2 = -320 + 320 + 480x + -480x

Combine like terms: -320 + 320 = 0
544 + -912x + 144x2 = 0 + 480x + -480x
544 + -912x + 144x2 = 480x + -480x

Combine like terms: 480x + -480x = 0
544 + -912x + 144x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(34 + -57x + 9x2) = 0

Factor a trinomial.
16((2 + -3x)(17 + -3x)) = 0

Ignore the factor 16.

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 '(17 + -3x)' equal to zero and attempt to solve:

Simplifying
17 + -3x = 0

Solving
17 + -3x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -3x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -3x = 0 + -17
-3x = 0 + -17

Combine like terms: 0 + -17 = -17
-3x = -17

Divide each side by '-3'.
x = 5.666666667

Simplifying
x = 5.666666667
Solution
x = {0.6666666667, 5.666666667}

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