(13x+7)(6x-18)=0

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Solution for (13x+7)(6x-18)=0 equation: 


Simplifying
(13x + 7)(6x + -18) = 0

Reorder the terms:
(7 + 13x)(6x + -18) = 0

Reorder the terms:
(7 + 13x)(-18 + 6x) = 0

Multiply (7 + 13x) * (-18 + 6x)
(7(-18 + 6x) + 13x * (-18 + 6x)) = 0
((-18 * 7 + 6x * 7) + 13x * (-18 + 6x)) = 0
((-126 + 42x) + 13x * (-18 + 6x)) = 0
(-126 + 42x + (-18 * 13x + 6x * 13x)) = 0
(-126 + 42x + (-234x + 78x2)) = 0

Combine like terms: 42x + -234x = -192x
(-126 + -192x + 78x2) = 0

Solving
-126 + -192x + 78x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + -32x + 13x2) = 0

Factor a trinomial.
6((-7 + -13x)(3 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-7 + -13x)' equal to zero and attempt to solve:

Simplifying
-7 + -13x = 0

Solving
-7 + -13x = 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 + -13x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13x = 0 + 7
-13x = 0 + 7

Combine like terms: 0 + 7 = 7
-13x = 7

Divide each side by '-13'.
x = -0.5384615385

Simplifying
x = -0.5384615385

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 = {-0.5384615385, 3}

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