3x(5-x)(4x+7)=0

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Solution for 3x(5-x)(4x+7)=0 equation:


Simplifying
3x(5 + -1x)(4x + 7) = 0

Reorder the terms:
3x(5 + -1x)(7 + 4x) = 0

Multiply (5 + -1x) * (7 + 4x)
3x(5(7 + 4x) + -1x * (7 + 4x)) = 0
3x((7 * 5 + 4x * 5) + -1x * (7 + 4x)) = 0
3x((35 + 20x) + -1x * (7 + 4x)) = 0
3x(35 + 20x + (7 * -1x + 4x * -1x)) = 0
3x(35 + 20x + (-7x + -4x2)) = 0

Combine like terms: 20x + -7x = 13x
3x(35 + 13x + -4x2) = 0
(35 * 3x + 13x * 3x + -4x2 * 3x) = 0
(105x + 39x2 + -12x3) = 0

Solving
105x + 39x2 + -12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(35 + 13x + -4x2) = 0

Factor a trinomial.
3x((5 + -1x)(7 + 4x)) = 0

Ignore the factor 3.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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, 5, -1.75}

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