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

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


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

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

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

Multiply (-9 + x) * (3 + 5x)
2(-9(3 + 5x) + x(3 + 5x)) = 0
2((3 * -9 + 5x * -9) + x(3 + 5x)) = 0
2((-27 + -45x) + x(3 + 5x)) = 0
2(-27 + -45x + (3 * x + 5x * x)) = 0
2(-27 + -45x + (3x + 5x2)) = 0

Combine like terms: -45x + 3x = -42x
2(-27 + -42x + 5x2) = 0
(-27 * 2 + -42x * 2 + 5x2 * 2) = 0
(-54 + -84x + 10x2) = 0

Solving
-54 + -84x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -42x + 5x2) = 0

Factor a trinomial.
2((-3 + -5x)(9 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.6, 9}

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