(5x-4)(x+9)=10x-66

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Solution for (5x-4)(x+9)=10x-66 equation: 


Simplifying
(5x + -4)(x + 9) = 10x + -66

Reorder the terms:
(-4 + 5x)(x + 9) = 10x + -66

Reorder the terms:
(-4 + 5x)(9 + x) = 10x + -66

Multiply (-4 + 5x) * (9 + x)
(-4(9 + x) + 5x * (9 + x)) = 10x + -66
((9 * -4 + x * -4) + 5x * (9 + x)) = 10x + -66
((-36 + -4x) + 5x * (9 + x)) = 10x + -66
(-36 + -4x + (9 * 5x + x * 5x)) = 10x + -66
(-36 + -4x + (45x + 5x2)) = 10x + -66

Combine like terms: -4x + 45x = 41x
(-36 + 41x + 5x2) = 10x + -66

Reorder the terms:
-36 + 41x + 5x2 = -66 + 10x

Solving
-36 + 41x + 5x2 = -66 + 10x

Solving for variable 'x'.

Reorder the terms:
-36 + 66 + 41x + -10x + 5x2 = -66 + 10x + 66 + -10x

Combine like terms: -36 + 66 = 30
30 + 41x + -10x + 5x2 = -66 + 10x + 66 + -10x

Combine like terms: 41x + -10x = 31x
30 + 31x + 5x2 = -66 + 10x + 66 + -10x

Reorder the terms:
30 + 31x + 5x2 = -66 + 66 + 10x + -10x

Combine like terms: -66 + 66 = 0
30 + 31x + 5x2 = 0 + 10x + -10x
30 + 31x + 5x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
30 + 31x + 5x2 = 0

Factor a trinomial.
(5 + x)(6 + 5x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Solution
x = {-5, -1.2}

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