2x^2+2x-15=x^2+10x+5

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Solution for 2x^2+2x-15=x^2+10x+5 equation:


Simplifying
2x2 + 2x + -15 = x2 + 10x + 5

Reorder the terms:
-15 + 2x + 2x2 = x2 + 10x + 5

Reorder the terms:
-15 + 2x + 2x2 = 5 + 10x + x2

Solving
-15 + 2x + 2x2 = 5 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-15 + -5 + 2x + -10x + 2x2 + -1x2 = 5 + 10x + x2 + -5 + -10x + -1x2

Combine like terms: -15 + -5 = -20
-20 + 2x + -10x + 2x2 + -1x2 = 5 + 10x + x2 + -5 + -10x + -1x2

Combine like terms: 2x + -10x = -8x
-20 + -8x + 2x2 + -1x2 = 5 + 10x + x2 + -5 + -10x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-20 + -8x + 1x2 = 5 + 10x + x2 + -5 + -10x + -1x2

Reorder the terms:
-20 + -8x + 1x2 = 5 + -5 + 10x + -10x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-20 + -8x + 1x2 = 0 + 10x + -10x + x2 + -1x2
-20 + -8x + 1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-20 + -8x + 1x2 = 0 + x2 + -1x2
-20 + -8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + -8x + 1x2 = 0

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


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 10}

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