4x(2x-3)(2x+25)=0

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Solution for 4x(2x-3)(2x+25)=0 equation: 


Simplifying
4x(2x + -3)(2x + 25) = 0

Reorder the terms:
4x(-3 + 2x)(2x + 25) = 0

Reorder the terms:
4x(-3 + 2x)(25 + 2x) = 0

Multiply (-3 + 2x) * (25 + 2x)
4x(-3(25 + 2x) + 2x * (25 + 2x)) = 0
4x((25 * -3 + 2x * -3) + 2x * (25 + 2x)) = 0
4x((-75 + -6x) + 2x * (25 + 2x)) = 0
4x(-75 + -6x + (25 * 2x + 2x * 2x)) = 0
4x(-75 + -6x + (50x + 4x2)) = 0

Combine like terms: -6x + 50x = 44x
4x(-75 + 44x + 4x2) = 0
(-75 * 4x + 44x * 4x + 4x2 * 4x) = 0
(-300x + 176x2 + 16x3) = 0

Solving
-300x + 176x2 + 16x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-75 + 44x + 4x2) = 0

Factor a trinomial.
4x((-25 + -2x)(3 + -2x)) = 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 '(-25 + -2x)' equal to zero and attempt to solve:

Simplifying
-25 + -2x = 0

Solving
-25 + -2x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2x = 0 + 25
-2x = 0 + 25

Combine like terms: 0 + 25 = 25
-2x = 25

Divide each side by '-2'.
x = -12.5

Simplifying
x = -12.5

Subproblem 3
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
Solution
x = {0, -12.5, 1.5}

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