(2x+13)(3x-7)=0

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Solution for (2x+13)(3x-7)=0 equation: 


Simplifying
(2x + 13)(3x + -7) = 0

Reorder the terms:
(13 + 2x)(3x + -7) = 0

Reorder the terms:
(13 + 2x)(-7 + 3x) = 0

Multiply (13 + 2x) * (-7 + 3x)
(13(-7 + 3x) + 2x * (-7 + 3x)) = 0
((-7 * 13 + 3x * 13) + 2x * (-7 + 3x)) = 0
((-91 + 39x) + 2x * (-7 + 3x)) = 0
(-91 + 39x + (-7 * 2x + 3x * 2x)) = 0
(-91 + 39x + (-14x + 6x2)) = 0

Combine like terms: 39x + -14x = 25x
(-91 + 25x + 6x2) = 0

Solving
-91 + 25x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + -2x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-6.5, 2.333333333}

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