(2x+5)(3x-9)=14x-56

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Solution for (2x+5)(3x-9)=14x-56 equation: 


Simplifying
(2x + 5)(3x + -9) = 14x + -56

Reorder the terms:
(5 + 2x)(3x + -9) = 14x + -56

Reorder the terms:
(5 + 2x)(-9 + 3x) = 14x + -56

Multiply (5 + 2x) * (-9 + 3x)
(5(-9 + 3x) + 2x * (-9 + 3x)) = 14x + -56
((-9 * 5 + 3x * 5) + 2x * (-9 + 3x)) = 14x + -56
((-45 + 15x) + 2x * (-9 + 3x)) = 14x + -56
(-45 + 15x + (-9 * 2x + 3x * 2x)) = 14x + -56
(-45 + 15x + (-18x + 6x2)) = 14x + -56

Combine like terms: 15x + -18x = -3x
(-45 + -3x + 6x2) = 14x + -56

Reorder the terms:
-45 + -3x + 6x2 = -56 + 14x

Solving
-45 + -3x + 6x2 = -56 + 14x

Solving for variable 'x'.

Reorder the terms:
-45 + 56 + -3x + -14x + 6x2 = -56 + 14x + 56 + -14x

Combine like terms: -45 + 56 = 11
11 + -3x + -14x + 6x2 = -56 + 14x + 56 + -14x

Combine like terms: -3x + -14x = -17x
11 + -17x + 6x2 = -56 + 14x + 56 + -14x

Reorder the terms:
11 + -17x + 6x2 = -56 + 56 + 14x + -14x

Combine like terms: -56 + 56 = 0
11 + -17x + 6x2 = 0 + 14x + -14x
11 + -17x + 6x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
11 + -17x + 6x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -6x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(11 + -6x)' equal to zero and attempt to solve:

Simplifying
11 + -6x = 0

Solving
11 + -6x = 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 + -6x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -6x = 0 + -11
-6x = 0 + -11

Combine like terms: 0 + -11 = -11
-6x = -11

Divide each side by '-6'.
x = 1.833333333

Simplifying
x = 1.833333333
Solution
x = {1, 1.833333333}

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