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

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


Simplifying
3(7 + -3x)(5x + 2) = 0

Reorder the terms:
3(7 + -3x)(2 + 5x) = 0

Multiply (7 + -3x) * (2 + 5x)
3(7(2 + 5x) + -3x * (2 + 5x)) = 0
3((2 * 7 + 5x * 7) + -3x * (2 + 5x)) = 0
3((14 + 35x) + -3x * (2 + 5x)) = 0
3(14 + 35x + (2 * -3x + 5x * -3x)) = 0
3(14 + 35x + (-6x + -15x2)) = 0

Combine like terms: 35x + -6x = 29x
3(14 + 29x + -15x2) = 0
(14 * 3 + 29x * 3 + -15x2 * 3) = 0
(42 + 87x + -45x2) = 0

Solving
42 + 87x + -45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + 29x + -15x2) = 0

Factor a trinomial.
3((7 + -3x)(2 + 5x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333

Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {2.333333333, -0.4}

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