x^2-100+(x-10)(x+3)=0

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Solution for x^2-100+(x-10)(x+3)=0 equation: 


Simplifying
x2 + -100 + (x + -10)(x + 3) = 0

Reorder the terms:
x2 + -100 + (-10 + x)(x + 3) = 0

Reorder the terms:
x2 + -100 + (-10 + x)(3 + x) = 0

Multiply (-10 + x) * (3 + x)
x2 + -100 + (-10(3 + x) + x(3 + x)) = 0
x2 + -100 + ((3 * -10 + x * -10) + x(3 + x)) = 0
x2 + -100 + ((-30 + -10x) + x(3 + x)) = 0
x2 + -100 + (-30 + -10x + (3 * x + x * x)) = 0
x2 + -100 + (-30 + -10x + (3x + x2)) = 0

Combine like terms: -10x + 3x = -7x
x2 + -100 + (-30 + -7x + x2) = 0

Reorder the terms:
-100 + -30 + -7x + x2 + x2 = 0

Combine like terms: -100 + -30 = -130
-130 + -7x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-130 + -7x + 2x2 = 0

Solving
-130 + -7x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + -2x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5

Subproblem 2
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
Solution
x = {-6.5, 10}

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