(2x+5)(9x-3)=0

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Solution for (2x+5)(9x-3)=0 equation: 


Simplifying
(2x + 5)(9x + -3) = 0

Reorder the terms:
(5 + 2x)(9x + -3) = 0

Reorder the terms:
(5 + 2x)(-3 + 9x) = 0

Multiply (5 + 2x) * (-3 + 9x)
(5(-3 + 9x) + 2x * (-3 + 9x)) = 0
((-3 * 5 + 9x * 5) + 2x * (-3 + 9x)) = 0
((-15 + 45x) + 2x * (-3 + 9x)) = 0
(-15 + 45x + (-3 * 2x + 9x * 2x)) = 0
(-15 + 45x + (-6x + 18x2)) = 0

Combine like terms: 45x + -6x = 39x
(-15 + 39x + 18x2) = 0

Solving
-15 + 39x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 13x + 6x2) = 0

Factor a trinomial.
3((-5 + -2x)(1 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
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 = {-2.5, 0.3333333333}

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