0=4x^2(5x-3)

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Solution for 0=4x^2(5x-3) equation: 


Simplifying
0 = 4x2(5x + -3)

Reorder the terms:
0 = 4x2(-3 + 5x)
0 = (-3 * 4x2 + 5x * 4x2)
0 = (-12x2 + 20x3)

Solving
0 = -12x2 + 20x3

Solving for variable 'x'.
Remove the zero:
12x2 + -20x3 = -12x2 + 20x3 + 12x2 + -20x3

Reorder the terms:
12x2 + -20x3 = -12x2 + 12x2 + 20x3 + -20x3

Combine like terms: -12x2 + 12x2 = 0
12x2 + -20x3 = 0 + 20x3 + -20x3
12x2 + -20x3 = 20x3 + -20x3

Combine like terms: 20x3 + -20x3 = 0
12x2 + -20x3 = 0

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(3 + -5x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0, 0.6}

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