(7x-5)(9x+3)=0

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Solution for (7x-5)(9x+3)=0 equation: 


Simplifying
(7x + -5)(9x + 3) = 0

Reorder the terms:
(-5 + 7x)(9x + 3) = 0

Reorder the terms:
(-5 + 7x)(3 + 9x) = 0

Multiply (-5 + 7x) * (3 + 9x)
(-5(3 + 9x) + 7x * (3 + 9x)) = 0
((3 * -5 + 9x * -5) + 7x * (3 + 9x)) = 0
((-15 + -45x) + 7x * (3 + 9x)) = 0
(-15 + -45x + (3 * 7x + 9x * 7x)) = 0
(-15 + -45x + (21x + 63x2)) = 0

Combine like terms: -45x + 21x = -24x
(-15 + -24x + 63x2) = 0

Solving
-15 + -24x + 63x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -8x + 21x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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
Solution
x = {-0.3333333333, 0.7142857143}

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