3(x^2+x-10)=2x^2-5(x+2)

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Solution for 3(x^2+x-10)=2x^2-5(x+2) equation: 


Simplifying
3(x2 + x + -10) = 2x2 + -5(x + 2)

Reorder the terms:
3(-10 + x + x2) = 2x2 + -5(x + 2)
(-10 * 3 + x * 3 + x2 * 3) = 2x2 + -5(x + 2)
(-30 + 3x + 3x2) = 2x2 + -5(x + 2)

Reorder the terms:
-30 + 3x + 3x2 = 2x2 + -5(2 + x)
-30 + 3x + 3x2 = 2x2 + (2 * -5 + x * -5)
-30 + 3x + 3x2 = 2x2 + (-10 + -5x)

Reorder the terms:
-30 + 3x + 3x2 = -10 + -5x + 2x2

Solving
-30 + 3x + 3x2 = -10 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-30 + 10 + 3x + 5x + 3x2 + -2x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Combine like terms: -30 + 10 = -20
-20 + 3x + 5x + 3x2 + -2x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Combine like terms: 3x + 5x = 8x
-20 + 8x + 3x2 + -2x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-20 + 8x + 1x2 = -10 + -5x + 2x2 + 10 + 5x + -2x2

Reorder the terms:
-20 + 8x + 1x2 = -10 + 10 + -5x + 5x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
-20 + 8x + 1x2 = 0 + -5x + 5x + 2x2 + -2x2
-20 + 8x + 1x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
-20 + 8x + 1x2 = 0 + 2x2 + -2x2
-20 + 8x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-20 + 8x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(2 + -1x) = 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 '(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
Solution
x = {-10, 2}

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