(x+4)(x-3)=x+37

Solution for (x+4)(x-3)=x+37 equation:

Simplifying
(x + 4)(x + -3) = x + 37

Reorder the terms:
(4 + x)(x + -3) = x + 37

Reorder the terms:
(4 + x)(-3 + x) = x + 37

Multiply (4 + x) * (-3 + x)
(4(-3 + x) + x(-3 + x)) = x + 37
((-3 * 4 + x * 4) + x(-3 + x)) = x + 37
((-12 + 4x) + x(-3 + x)) = x + 37
(-12 + 4x + (-3 * x + x * x)) = x + 37
(-12 + 4x + (-3x + x2)) = x + 37

Combine like terms: 4x + -3x = 1x
(-12 + 1x + x2) = x + 37

Reorder the terms:
-12 + 1x + x2 = 37 + x

Solving
-12 + 1x + x2 = 37 + x

Solving for variable 'x'.

Reorder the terms:
-12 + -37 + 1x + -1x + x2 = 37 + x + -37 + -1x

Combine like terms: -12 + -37 = -49
-49 + 1x + -1x + x2 = 37 + x + -37 + -1x

Combine like terms: 1x + -1x = 0
-49 + 0 + x2 = 37 + x + -37 + -1x
-49 + x2 = 37 + x + -37 + -1x

Reorder the terms:
-49 + x2 = 37 + -37 + x + -1x

Combine like terms: 37 + -37 = 0
-49 + x2 = 0 + x + -1x
-49 + x2 = x + -1x

Combine like terms: x + -1x = 0
-49 + x2 = 0

Factor a difference between two squares.
(7 + x)(-7 + x) = 0

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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7
Subproblem 2
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

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

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

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

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