(2x-3)(5x+15)=0

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Solution for (2x-3)(5x+15)=0 equation:


Simplifying
(2x + -3)(5x + 15) = 0

Reorder the terms:
(-3 + 2x)(5x + 15) = 0

Reorder the terms:
(-3 + 2x)(15 + 5x) = 0

Multiply (-3 + 2x) * (15 + 5x)
(-3(15 + 5x) + 2x * (15 + 5x)) = 0
((15 * -3 + 5x * -3) + 2x * (15 + 5x)) = 0
((-45 + -15x) + 2x * (15 + 5x)) = 0
(-45 + -15x + (15 * 2x + 5x * 2x)) = 0
(-45 + -15x + (30x + 10x2)) = 0

Combine like terms: -15x + 30x = 15x
(-45 + 15x + 10x2) = 0

Solving
-45 + 15x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + 3x + 2x2) = 0

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

Ignore the factor 5.

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-3, 1.5}

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