(2x+5)(x-9)=11-4x

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Solution for (2x+5)(x-9)=11-4x equation: 


Simplifying
(2x + 5)(x + -9) = 11 + -4x

Reorder the terms:
(5 + 2x)(x + -9) = 11 + -4x

Reorder the terms:
(5 + 2x)(-9 + x) = 11 + -4x

Multiply (5 + 2x) * (-9 + x)
(5(-9 + x) + 2x * (-9 + x)) = 11 + -4x
((-9 * 5 + x * 5) + 2x * (-9 + x)) = 11 + -4x
((-45 + 5x) + 2x * (-9 + x)) = 11 + -4x
(-45 + 5x + (-9 * 2x + x * 2x)) = 11 + -4x
(-45 + 5x + (-18x + 2x2)) = 11 + -4x

Combine like terms: 5x + -18x = -13x
(-45 + -13x + 2x2) = 11 + -4x

Solving
-45 + -13x + 2x2 = 11 + -4x

Solving for variable 'x'.

Reorder the terms:
-45 + -11 + -13x + 4x + 2x2 = 11 + -4x + -11 + 4x

Combine like terms: -45 + -11 = -56
-56 + -13x + 4x + 2x2 = 11 + -4x + -11 + 4x

Combine like terms: -13x + 4x = -9x
-56 + -9x + 2x2 = 11 + -4x + -11 + 4x

Reorder the terms:
-56 + -9x + 2x2 = 11 + -11 + -4x + 4x

Combine like terms: 11 + -11 = 0
-56 + -9x + 2x2 = 0 + -4x + 4x
-56 + -9x + 2x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-56 + -9x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3.5, 8}

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