(x-3)(x+4)=30

Solution for (x-3)(x+4)=30 equation:

Simplifying
(x + -3)(x + 4) = 30

Reorder the terms:
(-3 + x)(x + 4) = 30

Reorder the terms:
(-3 + x)(4 + x) = 30

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = 30
((4 * -3 + x * -3) + x(4 + x)) = 30
((-12 + -3x) + x(4 + x)) = 30
(-12 + -3x + (4 * x + x * x)) = 30
(-12 + -3x + (4x + x2)) = 30

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = 30

Solving
-12 + 1x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
-12 + -30 + 1x + x2 = 30 + -30

Combine like terms: -12 + -30 = -42
-42 + 1x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-42 + 1x + x2 = 0

Factor a trinomial.
(-7 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7, 6}