(5x-4)(5x+15)=0

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Solution for (5x-4)(5x+15)=0 equation:


Simplifying
(5x + -4)(5x + 15) = 0

Reorder the terms:
(-4 + 5x)(5x + 15) = 0

Reorder the terms:
(-4 + 5x)(15 + 5x) = 0

Multiply (-4 + 5x) * (15 + 5x)
(-4(15 + 5x) + 5x * (15 + 5x)) = 0
((15 * -4 + 5x * -4) + 5x * (15 + 5x)) = 0
((-60 + -20x) + 5x * (15 + 5x)) = 0
(-60 + -20x + (15 * 5x + 5x * 5x)) = 0
(-60 + -20x + (75x + 25x2)) = 0

Combine like terms: -20x + 75x = 55x
(-60 + 55x + 25x2) = 0

Solving
-60 + 55x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + 11x + 5x2) = 0

Factor a trinomial.
5((-3 + -1x)(4 + -5x)) = 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 '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8

Solution

x = {-3, 0.8}

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