(4x-101)(2x+3)x=

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Solution for (4x-101)(2x+3)x= equation: 


Simplifying
(4x + -101)(2x + 3) * x = 0

Reorder the terms:
(-101 + 4x)(2x + 3) * x = 0

Reorder the terms:
(-101 + 4x)(3 + 2x) * x = 0

Reorder the terms for easier multiplication:
x(-101 + 4x)(3 + 2x) = 0

Multiply (-101 + 4x) * (3 + 2x)
x(-101(3 + 2x) + 4x * (3 + 2x)) = 0
x((3 * -101 + 2x * -101) + 4x * (3 + 2x)) = 0
x((-303 + -202x) + 4x * (3 + 2x)) = 0
x(-303 + -202x + (3 * 4x + 2x * 4x)) = 0
x(-303 + -202x + (12x + 8x2)) = 0

Combine like terms: -202x + 12x = -190x
x(-303 + -190x + 8x2) = 0
(-303 * x + -190x * x + 8x2 * x) = 0
(-303x + -190x2 + 8x3) = 0

Solving
-303x + -190x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-303 + -190x + 8x2) = 0

Factor a trinomial.
x((-3 + -2x)(101 + -4x)) = 0


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 + -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 3
Set the factor '(101 + -4x)' equal to zero and attempt to solve:

Simplifying
101 + -4x = 0

Solving
101 + -4x = 0

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

Add '-101' to each side of the equation.
101 + -101 + -4x = 0 + -101

Combine like terms: 101 + -101 = 0
0 + -4x = 0 + -101
-4x = 0 + -101

Combine like terms: 0 + -101 = -101
-4x = -101

Divide each side by '-4'.
x = 25.25

Simplifying
x = 25.25
Solution
x = {0, -1.5, 25.25}

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