(10x+5)(15x-30)=0

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Solution for (10x+5)(15x-30)=0 equation: 


Simplifying
(10x + 5)(15x + -30) = 0

Reorder the terms:
(5 + 10x)(15x + -30) = 0

Reorder the terms:
(5 + 10x)(-30 + 15x) = 0

Multiply (5 + 10x) * (-30 + 15x)
(5(-30 + 15x) + 10x * (-30 + 15x)) = 0
((-30 * 5 + 15x * 5) + 10x * (-30 + 15x)) = 0
((-150 + 75x) + 10x * (-30 + 15x)) = 0
(-150 + 75x + (-30 * 10x + 15x * 10x)) = 0
(-150 + 75x + (-300x + 150x2)) = 0

Combine like terms: 75x + -300x = -225x
(-150 + -225x + 150x2) = 0

Solving
-150 + -225x + 150x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '75'.
75(-2 + -3x + 2x2) = 0

Factor a trinomial.
75((-1 + -2x)(2 + -1x)) = 0

Ignore the factor 75.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.5, 2}

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