(7x^2+5x)(3x-1)=0

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Solution for (7x^2+5x)(3x-1)=0 equation: 


Simplifying
(7x2 + 5x)(3x + -1) = 0

Reorder the terms:
(5x + 7x2)(3x + -1) = 0

Reorder the terms:
(5x + 7x2)(-1 + 3x) = 0

Multiply (5x + 7x2) * (-1 + 3x)
(5x * (-1 + 3x) + 7x2 * (-1 + 3x)) = 0
((-1 * 5x + 3x * 5x) + 7x2 * (-1 + 3x)) = 0
((-5x + 15x2) + 7x2 * (-1 + 3x)) = 0
(-5x + 15x2 + (-1 * 7x2 + 3x * 7x2)) = 0
(-5x + 15x2 + (-7x2 + 21x3)) = 0

Combine like terms: 15x2 + -7x2 = 8x2
(-5x + 8x2 + 21x3) = 0

Solving
-5x + 8x2 + 21x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 8x + 21x2) = 0

Factor a trinomial.
x((-5 + -7x)(1 + -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 '(-5 + -7x)' equal to zero and attempt to solve:

Simplifying
-5 + -7x = 0

Solving
-5 + -7x = 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 + -7x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7x = 0 + 5
-7x = 0 + 5

Combine like terms: 0 + 5 = 5
-7x = 5

Divide each side by '-7'.
x = -0.7142857143

Simplifying
x = -0.7142857143

Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -0.7142857143, 0.3333333333}

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