(x-10)(x+4)=-45

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Solution for (x-10)(x+4)=-45 equation: 


Simplifying
(x + -10)(x + 4) = -45

Reorder the terms:
(-10 + x)(x + 4) = -45

Reorder the terms:
(-10 + x)(4 + x) = -45

Multiply (-10 + x) * (4 + x)
(-10(4 + x) + x(4 + x)) = -45
((4 * -10 + x * -10) + x(4 + x)) = -45
((-40 + -10x) + x(4 + x)) = -45
(-40 + -10x + (4 * x + x * x)) = -45
(-40 + -10x + (4x + x2)) = -45

Combine like terms: -10x + 4x = -6x
(-40 + -6x + x2) = -45

Solving
-40 + -6x + x2 = -45

Solving for variable 'x'.

Reorder the terms:
-40 + 45 + -6x + x2 = -45 + 45

Combine like terms: -40 + 45 = 5
5 + -6x + x2 = -45 + 45

Combine like terms: -45 + 45 = 0
5 + -6x + x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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