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

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


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

Multiply 5 * 3
(15x + 3)(x * 3 + -7) = 0

Reorder the terms:
(3 + 15x)(x * 3 + -7) = 0

Reorder the terms for easier multiplication:
(3 + 15x)(3x + -7) = 0

Reorder the terms:
(3 + 15x)(-7 + 3x) = 0

Multiply (3 + 15x) * (-7 + 3x)
(3(-7 + 3x) + 15x * (-7 + 3x)) = 0
((-7 * 3 + 3x * 3) + 15x * (-7 + 3x)) = 0
((-21 + 9x) + 15x * (-7 + 3x)) = 0
(-21 + 9x + (-7 * 15x + 3x * 15x)) = 0
(-21 + 9x + (-105x + 45x2)) = 0

Combine like terms: 9x + -105x = -96x
(-21 + -96x + 45x2) = 0

Solving
-21 + -96x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -32x + 15x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

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

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

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2

Subproblem 2
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
Solution
x = {-0.2, 2.333333333}

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