(7x-49)(2x-13)=0

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Solution for (7x-49)(2x-13)=0 equation: 


Simplifying
(7x + -49)(2x + -13) = 0

Reorder the terms:
(-49 + 7x)(2x + -13) = 0

Reorder the terms:
(-49 + 7x)(-13 + 2x) = 0

Multiply (-49 + 7x) * (-13 + 2x)
(-49(-13 + 2x) + 7x * (-13 + 2x)) = 0
((-13 * -49 + 2x * -49) + 7x * (-13 + 2x)) = 0
((637 + -98x) + 7x * (-13 + 2x)) = 0
(637 + -98x + (-13 * 7x + 2x * 7x)) = 0
(637 + -98x + (-91x + 14x2)) = 0

Combine like terms: -98x + -91x = -189x
(637 + -189x + 14x2) = 0

Solving
637 + -189x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(91 + -27x + 2x2) = 0

Factor a trinomial.
7((13 + -2x)(7 + -1x)) = 0

Ignore the factor 7.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {6.5, 7}

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