(3x-5)x(7x+10)=

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Solution for (3x-5)x(7x+10)= equation: 


Simplifying
(3x + -5) * x(7x + 10) = 0

Reorder the terms:
(-5 + 3x) * x(7x + 10) = 0

Reorder the terms:
(-5 + 3x) * x(10 + 7x) = 0

Reorder the terms for easier multiplication:
x(-5 + 3x)(10 + 7x) = 0

Multiply (-5 + 3x) * (10 + 7x)
x(-5(10 + 7x) + 3x * (10 + 7x)) = 0
x((10 * -5 + 7x * -5) + 3x * (10 + 7x)) = 0
x((-50 + -35x) + 3x * (10 + 7x)) = 0
x(-50 + -35x + (10 * 3x + 7x * 3x)) = 0
x(-50 + -35x + (30x + 21x2)) = 0

Combine like terms: -35x + 30x = -5x
x(-50 + -5x + 21x2) = 0
(-50 * x + -5x * x + 21x2 * x) = 0
(-50x + -5x2 + 21x3) = 0

Solving
-50x + -5x2 + 21x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-50 + -5x + 21x2) = 0

Factor a trinomial.
x((-10 + -7x)(5 + -3x)) = 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 '(-10 + -7x)' equal to zero and attempt to solve:

Simplifying
-10 + -7x = 0

Solving
-10 + -7x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -7x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -7x = 0 + 10
-7x = 0 + 10

Combine like terms: 0 + 10 = 10
-7x = 10

Divide each side by '-7'.
x = -1.428571429

Simplifying
x = -1.428571429

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

Simplifying
5 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, -1.428571429, 1.666666667}

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