(4x+5)(5x-4)=x+13

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Solution for (4x+5)(5x-4)=x+13 equation: 


Simplifying
(4x + 5)(5x + -4) = x + 13

Reorder the terms:
(5 + 4x)(5x + -4) = x + 13

Reorder the terms:
(5 + 4x)(-4 + 5x) = x + 13

Multiply (5 + 4x) * (-4 + 5x)
(5(-4 + 5x) + 4x * (-4 + 5x)) = x + 13
((-4 * 5 + 5x * 5) + 4x * (-4 + 5x)) = x + 13
((-20 + 25x) + 4x * (-4 + 5x)) = x + 13
(-20 + 25x + (-4 * 4x + 5x * 4x)) = x + 13
(-20 + 25x + (-16x + 20x2)) = x + 13

Combine like terms: 25x + -16x = 9x
(-20 + 9x + 20x2) = x + 13

Reorder the terms:
-20 + 9x + 20x2 = 13 + x

Solving
-20 + 9x + 20x2 = 13 + x

Solving for variable 'x'.

Reorder the terms:
-20 + -13 + 9x + -1x + 20x2 = 13 + x + -13 + -1x

Combine like terms: -20 + -13 = -33
-33 + 9x + -1x + 20x2 = 13 + x + -13 + -1x

Combine like terms: 9x + -1x = 8x
-33 + 8x + 20x2 = 13 + x + -13 + -1x

Reorder the terms:
-33 + 8x + 20x2 = 13 + -13 + x + -1x

Combine like terms: 13 + -13 = 0
-33 + 8x + 20x2 = 0 + x + -1x
-33 + 8x + 20x2 = x + -1x

Combine like terms: x + -1x = 0
-33 + 8x + 20x2 = 0

Factor a trinomial.
(-3 + -2x)(11 + -10x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(11 + -10x)' equal to zero and attempt to solve:

Simplifying
11 + -10x = 0

Solving
11 + -10x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -10x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10x = 0 + -11
-10x = 0 + -11

Combine like terms: 0 + -11 = -11
-10x = -11

Divide each side by '-10'.
x = 1.1

Simplifying
x = 1.1
Solution
x = {-1.5, 1.1}

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