3x^2-6x-100=-18x+35

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Solution for 3x^2-6x-100=-18x+35 equation:


Simplifying
3x2 + -6x + -100 = -18x + 35

Reorder the terms:
-100 + -6x + 3x2 = -18x + 35

Reorder the terms:
-100 + -6x + 3x2 = 35 + -18x

Solving
-100 + -6x + 3x2 = 35 + -18x

Solving for variable 'x'.

Reorder the terms:
-100 + -35 + -6x + 18x + 3x2 = 35 + -18x + -35 + 18x

Combine like terms: -100 + -35 = -135
-135 + -6x + 18x + 3x2 = 35 + -18x + -35 + 18x

Combine like terms: -6x + 18x = 12x
-135 + 12x + 3x2 = 35 + -18x + -35 + 18x

Reorder the terms:
-135 + 12x + 3x2 = 35 + -35 + -18x + 18x

Combine like terms: 35 + -35 = 0
-135 + 12x + 3x2 = 0 + -18x + 18x
-135 + 12x + 3x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
-135 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-45 + 4x + x2) = 0

Factor a trinomial.
3((-9 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-9, 5}

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