(27-13x)*(5-x)=40x

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Solution for (27-13x)*(5-x)=40x equation: 


Simplifying
(27 + -13x)(5 + -1x) = 40x

Multiply (27 + -13x) * (5 + -1x)
(27(5 + -1x) + -13x * (5 + -1x)) = 40x
((5 * 27 + -1x * 27) + -13x * (5 + -1x)) = 40x
((135 + -27x) + -13x * (5 + -1x)) = 40x
(135 + -27x + (5 * -13x + -1x * -13x)) = 40x
(135 + -27x + (-65x + 13x2)) = 40x

Combine like terms: -27x + -65x = -92x
(135 + -92x + 13x2) = 40x

Solving
135 + -92x + 13x2 = 40x

Solving for variable 'x'.

Reorder the terms:
135 + -92x + -40x + 13x2 = 40x + -40x

Combine like terms: -92x + -40x = -132x
135 + -132x + 13x2 = 40x + -40x

Combine like terms: 40x + -40x = 0
135 + -132x + 13x2 = 0

Factor a trinomial.
(15 + -13x)(9 + -1x) = 0


Subproblem 1
Set the factor '(15 + -13x)' equal to zero and attempt to solve:

Simplifying
15 + -13x = 0

Solving
15 + -13x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -13x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -13x = 0 + -15
-13x = 0 + -15

Combine like terms: 0 + -15 = -15
-13x = -15

Divide each side by '-13'.
x = 1.153846154

Simplifying
x = 1.153846154

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {1.153846154, 9}

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