x^2+6x-40=(2x+5)(x-8)

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Solution for x^2+6x-40=(2x+5)(x-8) equation:


Simplifying
x2 + 6x + -40 = (2x + 5)(x + -8)

Reorder the terms:
-40 + 6x + x2 = (2x + 5)(x + -8)

Reorder the terms:
-40 + 6x + x2 = (5 + 2x)(x + -8)

Reorder the terms:
-40 + 6x + x2 = (5 + 2x)(-8 + x)

Multiply (5 + 2x) * (-8 + x)
-40 + 6x + x2 = (5(-8 + x) + 2x * (-8 + x))
-40 + 6x + x2 = ((-8 * 5 + x * 5) + 2x * (-8 + x))
-40 + 6x + x2 = ((-40 + 5x) + 2x * (-8 + x))
-40 + 6x + x2 = (-40 + 5x + (-8 * 2x + x * 2x))
-40 + 6x + x2 = (-40 + 5x + (-16x + 2x2))

Combine like terms: 5x + -16x = -11x
-40 + 6x + x2 = (-40 + -11x + 2x2)

Add '40' to each side of the equation.
-40 + 6x + 40 + x2 = -40 + -11x + 40 + 2x2

Reorder the terms:
-40 + 40 + 6x + x2 = -40 + -11x + 40 + 2x2

Combine like terms: -40 + 40 = 0
0 + 6x + x2 = -40 + -11x + 40 + 2x2
6x + x2 = -40 + -11x + 40 + 2x2

Reorder the terms:
6x + x2 = -40 + 40 + -11x + 2x2

Combine like terms: -40 + 40 = 0
6x + x2 = 0 + -11x + 2x2
6x + x2 = -11x + 2x2

Solving
6x + x2 = -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
6x + 11x + x2 + -2x2 = -11x + 2x2 + 11x + -2x2

Combine like terms: 6x + 11x = 17x
17x + x2 + -2x2 = -11x + 2x2 + 11x + -2x2

Combine like terms: x2 + -2x2 = -1x2
17x + -1x2 = -11x + 2x2 + 11x + -2x2

Reorder the terms:
17x + -1x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
17x + -1x2 = 0 + 2x2 + -2x2
17x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
17x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(17 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {0, 17}

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