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

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


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

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

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

Multiply (-3 + 2x) * (9 + 5x)
(-3(9 + 5x) + 2x * (9 + 5x)) = 0
((9 * -3 + 5x * -3) + 2x * (9 + 5x)) = 0
((-27 + -15x) + 2x * (9 + 5x)) = 0
(-27 + -15x + (9 * 2x + 5x * 2x)) = 0
(-27 + -15x + (18x + 10x2)) = 0

Combine like terms: -15x + 18x = 3x
(-27 + 3x + 10x2) = 0

Solving
-27 + 3x + 10x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-9 + -5x)' equal to zero and attempt to solve: Simplifying -9 + -5x = 0 Solving -9 + -5x = 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 + -5x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5x = 0 + 9 -5x = 0 + 9 Combine like terms: 0 + 9 = 9 -5x = 9 Divide each side by '-5'. x = -1.8 Simplifying x = -1.8

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 = {-1.8, 1.5}

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