2(x+5)(x-2)=x(x+5)+90

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Solution for 2(x+5)(x-2)=x(x+5)+90 equation: 


Simplifying
2(x + 5)(x + -2) = x(x + 5) + 90

Reorder the terms:
2(5 + x)(x + -2) = x(x + 5) + 90

Reorder the terms:
2(5 + x)(-2 + x) = x(x + 5) + 90

Multiply (5 + x) * (-2 + x)
2(5(-2 + x) + x(-2 + x)) = x(x + 5) + 90
2((-2 * 5 + x * 5) + x(-2 + x)) = x(x + 5) + 90
2((-10 + 5x) + x(-2 + x)) = x(x + 5) + 90
2(-10 + 5x + (-2 * x + x * x)) = x(x + 5) + 90
2(-10 + 5x + (-2x + x2)) = x(x + 5) + 90

Combine like terms: 5x + -2x = 3x
2(-10 + 3x + x2) = x(x + 5) + 90
(-10 * 2 + 3x * 2 + x2 * 2) = x(x + 5) + 90
(-20 + 6x + 2x2) = x(x + 5) + 90

Reorder the terms:
-20 + 6x + 2x2 = x(5 + x) + 90
-20 + 6x + 2x2 = (5 * x + x * x) + 90
-20 + 6x + 2x2 = (5x + x2) + 90

Reorder the terms:
-20 + 6x + 2x2 = 90 + 5x + x2

Solving
-20 + 6x + 2x2 = 90 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + -90 + 6x + -5x + 2x2 + -1x2 = 90 + 5x + x2 + -90 + -5x + -1x2

Combine like terms: -20 + -90 = -110
-110 + 6x + -5x + 2x2 + -1x2 = 90 + 5x + x2 + -90 + -5x + -1x2

Combine like terms: 6x + -5x = 1x
-110 + 1x + 2x2 + -1x2 = 90 + 5x + x2 + -90 + -5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-110 + 1x + 1x2 = 90 + 5x + x2 + -90 + -5x + -1x2

Reorder the terms:
-110 + 1x + 1x2 = 90 + -90 + 5x + -5x + x2 + -1x2

Combine like terms: 90 + -90 = 0
-110 + 1x + 1x2 = 0 + 5x + -5x + x2 + -1x2
-110 + 1x + 1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-110 + 1x + 1x2 = 0 + x2 + -1x2
-110 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-110 + 1x + 1x2 = 0

Factor a trinomial.
(-11 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

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 = {-11, 10}

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