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

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


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

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

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

Multiply (-7 + 4x) * (3 + 8x)
4x(-7(3 + 8x) + 4x * (3 + 8x)) = 0
4x((3 * -7 + 8x * -7) + 4x * (3 + 8x)) = 0
4x((-21 + -56x) + 4x * (3 + 8x)) = 0
4x(-21 + -56x + (3 * 4x + 8x * 4x)) = 0
4x(-21 + -56x + (12x + 32x2)) = 0

Combine like terms: -56x + 12x = -44x
4x(-21 + -44x + 32x2) = 0
(-21 * 4x + -44x * 4x + 32x2 * 4x) = 0
(-84x + -176x2 + 128x3) = 0

Solving
-84x + -176x2 + 128x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-21 + -44x + 32x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-3 + -8x = 0

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

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

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

Divide each side by '-8'.
x = -0.375

Simplifying
x = -0.375

Subproblem 3
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {0, -0.375, 1.75}

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