(x+10)(x-4)=-33

Solution for (x+10)(x-4)=-33 equation:

Simplifying
(x + 10)(x + -4) = -33

Reorder the terms:
(10 + x)(x + -4) = -33

Reorder the terms:
(10 + x)(-4 + x) = -33

Multiply (10 + x) * (-4 + x)
(10(-4 + x) + x(-4 + x)) = -33
((-4 * 10 + x * 10) + x(-4 + x)) = -33
((-40 + 10x) + x(-4 + x)) = -33
(-40 + 10x + (-4 * x + x * x)) = -33
(-40 + 10x + (-4x + x2)) = -33

Combine like terms: 10x + -4x = 6x
(-40 + 6x + x2) = -33

Solving
-40 + 6x + x2 = -33

Solving for variable 'x'.

Reorder the terms:
-40 + 33 + 6x + x2 = -33 + 33

Combine like terms: -40 + 33 = -7
-7 + 6x + x2 = -33 + 33

Combine like terms: -33 + 33 = 0
-7 + 6x + x2 = 0

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

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

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
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
Solution
x = {-7, 1}