4(2x-3)(3x-8)=0

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Solution for 4(2x-3)(3x-8)=0 equation: 


Simplifying
4(2x + -3)(3x + -8) = 0

Reorder the terms:
4(-3 + 2x)(3x + -8) = 0

Reorder the terms:
4(-3 + 2x)(-8 + 3x) = 0

Multiply (-3 + 2x) * (-8 + 3x)
4(-3(-8 + 3x) + 2x * (-8 + 3x)) = 0
4((-8 * -3 + 3x * -3) + 2x * (-8 + 3x)) = 0
4((24 + -9x) + 2x * (-8 + 3x)) = 0
4(24 + -9x + (-8 * 2x + 3x * 2x)) = 0
4(24 + -9x + (-16x + 6x2)) = 0

Combine like terms: -9x + -16x = -25x
4(24 + -25x + 6x2) = 0
(24 * 4 + -25x * 4 + 6x2 * 4) = 0
(96 + -100x + 24x2) = 0

Solving
96 + -100x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + -25x + 6x2) = 0

Factor a trinomial.
4((3 + -2x)(8 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {1.5, 2.666666667}

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