(X+4)(X-3)=78

Solution for (X+4)(X-3)=78 equation:

Simplifying
(X + 4)(X + -3) = 78

Reorder the terms:
(4 + X)(X + -3) = 78

Reorder the terms:
(4 + X)(-3 + X) = 78

Multiply (4 + X) * (-3 + X)
(4(-3 + X) + X(-3 + X)) = 78
((-3 * 4 + X * 4) + X(-3 + X)) = 78
((-12 + 4X) + X(-3 + X)) = 78
(-12 + 4X + (-3 * X + X * X)) = 78
(-12 + 4X + (-3X + X2)) = 78

Combine like terms: 4X + -3X = 1X
(-12 + 1X + X2) = 78

Solving
-12 + 1X + X2 = 78

Solving for variable 'X'.

Reorder the terms:
-12 + -78 + 1X + X2 = 78 + -78

Combine like terms: -12 + -78 = -90
-90 + 1X + X2 = 78 + -78

Combine like terms: 78 + -78 = 0
-90 + 1X + X2 = 0

Factor a trinomial.
(-10 + -1X)(9 + -1X) = 0

Subproblem 1
Set the factor '(-10 + -1X)' equal to zero and attempt to solve:

Simplifying
-10 + -1X = 0

Solving
-10 + -1X = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1X = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1X = 0 + 10
-1X = 0 + 10

Combine like terms: 0 + 10 = 10
-1X = 10

Divide each side by '-1'.
X = -10

Simplifying
X = -10
Subproblem 2
Set the factor '(9 + -1X)' equal to zero and attempt to solve:

Simplifying
9 + -1X = 0

Solving
9 + -1X = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1X = 0 + -9
-1X = 0 + -9

Combine like terms: 0 + -9 = -9
-1X = -9

Divide each side by '-1'.
X = 9

Simplifying
X = 9
Solution
X = {-10, 9}