0=(2x+5)(x-6)-x^2

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Solution for 0=(2x+5)(x-6)-x^2 equation: 


Simplifying
0 = (2x + 5)(x + -6) + -1x2

Reorder the terms:
0 = (5 + 2x)(x + -6) + -1x2

Reorder the terms:
0 = (5 + 2x)(-6 + x) + -1x2

Multiply (5 + 2x) * (-6 + x)
0 = (5(-6 + x) + 2x * (-6 + x)) + -1x2
0 = ((-6 * 5 + x * 5) + 2x * (-6 + x)) + -1x2
0 = ((-30 + 5x) + 2x * (-6 + x)) + -1x2
0 = (-30 + 5x + (-6 * 2x + x * 2x)) + -1x2
0 = (-30 + 5x + (-12x + 2x2)) + -1x2

Combine like terms: 5x + -12x = -7x
0 = (-30 + -7x + 2x2) + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
0 = -30 + -7x + 1x2

Solving
0 = -30 + -7x + 1x2

Solving for variable 'x'.

Combine like terms: 0 + 30 = 30
30 + 7x + -1x2 = -30 + -7x + 1x2 + 30 + 7x + -1x2

Reorder the terms:
30 + 7x + -1x2 = -30 + 30 + -7x + 7x + 1x2 + -1x2

Combine like terms: -30 + 30 = 0
30 + 7x + -1x2 = 0 + -7x + 7x + 1x2 + -1x2
30 + 7x + -1x2 = -7x + 7x + 1x2 + -1x2

Combine like terms: -7x + 7x = 0
30 + 7x + -1x2 = 0 + 1x2 + -1x2
30 + 7x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
30 + 7x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {10, -3}

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