(x+4)*(x-3)=-10

Solution for (x+4)*(x-3)=-10 equation:

Simplifying
(x + 4)(x + -3) = -10

Reorder the terms:
(4 + x)(x + -3) = -10

Reorder the terms:
(4 + x)(-3 + x) = -10

Multiply (4 + x) * (-3 + x)
(4(-3 + x) + x(-3 + x)) = -10
((-3 * 4 + x * 4) + x(-3 + x)) = -10
((-12 + 4x) + x(-3 + x)) = -10
(-12 + 4x + (-3 * x + x * x)) = -10
(-12 + 4x + (-3x + x2)) = -10

Combine like terms: 4x + -3x = 1x
(-12 + 1x + x2) = -10

Solving
-12 + 1x + x2 = -10

Solving for variable 'x'.

Reorder the terms:
-12 + 10 + 1x + x2 = -10 + 10

Combine like terms: -12 + 10 = -2
-2 + 1x + x2 = -10 + 10

Combine like terms: -10 + 10 = 0
-2 + 1x + x2 = 0

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

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 1}