x^2+8x-30=3x(x-8)

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Solution for x^2+8x-30=3x(x-8) equation: 


Simplifying
x2 + 8x + -30 = 3x(x + -8)

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

Reorder the terms:
-30 + 8x + x2 = 3x(-8 + x)
-30 + 8x + x2 = (-8 * 3x + x * 3x)
-30 + 8x + x2 = (-24x + 3x2)

Solving
-30 + 8x + x2 = -24x + 3x2

Solving for variable 'x'.

Reorder the terms:
-30 + 8x + 24x + x2 + -3x2 = -24x + 3x2 + 24x + -3x2

Combine like terms: 8x + 24x = 32x
-30 + 32x + x2 + -3x2 = -24x + 3x2 + 24x + -3x2

Combine like terms: x2 + -3x2 = -2x2
-30 + 32x + -2x2 = -24x + 3x2 + 24x + -3x2

Reorder the terms:
-30 + 32x + -2x2 = -24x + 24x + 3x2 + -3x2

Combine like terms: -24x + 24x = 0
-30 + 32x + -2x2 = 0 + 3x2 + -3x2
-30 + 32x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-30 + 32x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 16x + -1x2) = 0

Factor a trinomial.
2((-15 + x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + x)' equal to zero and attempt to solve:

Simplifying
-15 + x = 0

Solving
-15 + x = 0

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

Add '15' to each side of the equation.
-15 + 15 + x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + x = 0 + 15
x = 0 + 15

Combine like terms: 0 + 15 = 15
x = 15

Simplifying
x = 15

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {15, 1}

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