(13x+8)(5x-15)=0

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Solution for (13x+8)(5x-15)=0 equation: 


Simplifying
(13x + 8)(5x + -15) = 0

Reorder the terms:
(8 + 13x)(5x + -15) = 0

Reorder the terms:
(8 + 13x)(-15 + 5x) = 0

Multiply (8 + 13x) * (-15 + 5x)
(8(-15 + 5x) + 13x * (-15 + 5x)) = 0
((-15 * 8 + 5x * 8) + 13x * (-15 + 5x)) = 0
((-120 + 40x) + 13x * (-15 + 5x)) = 0
(-120 + 40x + (-15 * 13x + 5x * 13x)) = 0
(-120 + 40x + (-195x + 65x2)) = 0

Combine like terms: 40x + -195x = -155x
(-120 + -155x + 65x2) = 0

Solving
-120 + -155x + 65x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + -31x + 13x2) = 0

Factor a trinomial.
5((-8 + -13x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-8 + -13x)' equal to zero and attempt to solve:

Simplifying
-8 + -13x = 0

Solving
-8 + -13x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -13x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -13x = 0 + 8
-13x = 0 + 8

Combine like terms: 0 + 8 = 8
-13x = 8

Divide each side by '-13'.
x = -0.6153846154

Simplifying
x = -0.6153846154

Subproblem 2
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
Solution
x = {-0.6153846154, 3}

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