10+2x=15+25x-18x-30x^2

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Solution for 10+2x=15+25x-18x-30x^2 equation: 


Simplifying
10 + 2x = 15 + 25x + -18x + -30x2

Combine like terms: 25x + -18x = 7x
10 + 2x = 15 + 7x + -30x2

Solving
10 + 2x = 15 + 7x + -30x2

Solving for variable 'x'.

Reorder the terms:
10 + -15 + 2x + -7x + 30x2 = 15 + 7x + -30x2 + -15 + -7x + 30x2

Combine like terms: 10 + -15 = -5
-5 + 2x + -7x + 30x2 = 15 + 7x + -30x2 + -15 + -7x + 30x2

Combine like terms: 2x + -7x = -5x
-5 + -5x + 30x2 = 15 + 7x + -30x2 + -15 + -7x + 30x2

Reorder the terms:
-5 + -5x + 30x2 = 15 + -15 + 7x + -7x + -30x2 + 30x2

Combine like terms: 15 + -15 = 0
-5 + -5x + 30x2 = 0 + 7x + -7x + -30x2 + 30x2
-5 + -5x + 30x2 = 7x + -7x + -30x2 + 30x2

Combine like terms: 7x + -7x = 0
-5 + -5x + 30x2 = 0 + -30x2 + 30x2
-5 + -5x + 30x2 = -30x2 + 30x2

Combine like terms: -30x2 + 30x2 = 0
-5 + -5x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + -1x + 6x2) = 0

Factor a trinomial.
5((-1 + -3x)(1 + -2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.3333333333, 0.5}

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