8(3x-4)(2x-7)=0

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Solution for 8(3x-4)(2x-7)=0 equation: 


Simplifying
8(3x + -4)(2x + -7) = 0

Reorder the terms:
8(-4 + 3x)(2x + -7) = 0

Reorder the terms:
8(-4 + 3x)(-7 + 2x) = 0

Multiply (-4 + 3x) * (-7 + 2x)
8(-4(-7 + 2x) + 3x * (-7 + 2x)) = 0
8((-7 * -4 + 2x * -4) + 3x * (-7 + 2x)) = 0
8((28 + -8x) + 3x * (-7 + 2x)) = 0
8(28 + -8x + (-7 * 3x + 2x * 3x)) = 0
8(28 + -8x + (-21x + 6x2)) = 0

Combine like terms: -8x + -21x = -29x
8(28 + -29x + 6x2) = 0
(28 * 8 + -29x * 8 + 6x2 * 8) = 0
(224 + -232x + 48x2) = 0

Solving
224 + -232x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(28 + -29x + 6x2) = 0

Factor a trinomial.
8((4 + -3x)(7 + -2x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {1.333333333, 3.5}

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