-3x^2-30x=-40-8x^2

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Solution for -3x^2-30x=-40-8x^2 equation: 


Simplifying
-3x2 + -30x = -40 + -8x2

Reorder the terms:
-30x + -3x2 = -40 + -8x2

Solving
-30x + -3x2 = -40 + -8x2

Solving for variable 'x'.

Reorder the terms:
40 + -30x + -3x2 + 8x2 = -40 + -8x2 + 40 + 8x2

Combine like terms: -3x2 + 8x2 = 5x2
40 + -30x + 5x2 = -40 + -8x2 + 40 + 8x2

Reorder the terms:
40 + -30x + 5x2 = -40 + 40 + -8x2 + 8x2

Combine like terms: -40 + 40 = 0
40 + -30x + 5x2 = 0 + -8x2 + 8x2
40 + -30x + 5x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
40 + -30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(8 + -6x + x2) = 0

Factor a trinomial.
5((2 + -1x)(4 + -1x)) = 0

Ignore the factor 5.

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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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