0=(x+6)(x-3)-52

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Solution for 0=(x+6)(x-3)-52 equation: 


Simplifying
0 = (x + 6)(x + -3) + -52

Reorder the terms:
0 = (6 + x)(x + -3) + -52

Reorder the terms:
0 = (6 + x)(-3 + x) + -52

Multiply (6 + x) * (-3 + x)
0 = (6(-3 + x) + x(-3 + x)) + -52
0 = ((-3 * 6 + x * 6) + x(-3 + x)) + -52
0 = ((-18 + 6x) + x(-3 + x)) + -52
0 = (-18 + 6x + (-3 * x + x * x)) + -52
0 = (-18 + 6x + (-3x + x2)) + -52

Combine like terms: 6x + -3x = 3x
0 = (-18 + 3x + x2) + -52

Reorder the terms:
0 = -18 + -52 + 3x + x2

Combine like terms: -18 + -52 = -70
0 = -70 + 3x + x2

Solving
0 = -70 + 3x + x2

Solving for variable 'x'.

Combine like terms: 0 + 70 = 70
70 + -3x + -1x2 = -70 + 3x + x2 + 70 + -3x + -1x2

Reorder the terms:
70 + -3x + -1x2 = -70 + 70 + 3x + -3x + x2 + -1x2

Combine like terms: -70 + 70 = 0
70 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
70 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
70 + -3x + -1x2 = 0 + x2 + -1x2
70 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
70 + -3x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {7, -10}

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