(5x+17)(x-10)=(4x+15)(x-11)

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Solution for (5x+17)(x-10)=(4x+15)(x-11) equation: 


Simplifying
(5x + 17)(x + -10) = (4x + 15)(x + -11)

Reorder the terms:
(17 + 5x)(x + -10) = (4x + 15)(x + -11)

Reorder the terms:
(17 + 5x)(-10 + x) = (4x + 15)(x + -11)

Multiply (17 + 5x) * (-10 + x)
(17(-10 + x) + 5x * (-10 + x)) = (4x + 15)(x + -11)
((-10 * 17 + x * 17) + 5x * (-10 + x)) = (4x + 15)(x + -11)
((-170 + 17x) + 5x * (-10 + x)) = (4x + 15)(x + -11)
(-170 + 17x + (-10 * 5x + x * 5x)) = (4x + 15)(x + -11)
(-170 + 17x + (-50x + 5x2)) = (4x + 15)(x + -11)

Combine like terms: 17x + -50x = -33x
(-170 + -33x + 5x2) = (4x + 15)(x + -11)

Reorder the terms:
-170 + -33x + 5x2 = (15 + 4x)(x + -11)

Reorder the terms:
-170 + -33x + 5x2 = (15 + 4x)(-11 + x)

Multiply (15 + 4x) * (-11 + x)
-170 + -33x + 5x2 = (15(-11 + x) + 4x * (-11 + x))
-170 + -33x + 5x2 = ((-11 * 15 + x * 15) + 4x * (-11 + x))
-170 + -33x + 5x2 = ((-165 + 15x) + 4x * (-11 + x))
-170 + -33x + 5x2 = (-165 + 15x + (-11 * 4x + x * 4x))
-170 + -33x + 5x2 = (-165 + 15x + (-44x + 4x2))

Combine like terms: 15x + -44x = -29x
-170 + -33x + 5x2 = (-165 + -29x + 4x2)

Solving
-170 + -33x + 5x2 = -165 + -29x + 4x2

Solving for variable 'x'.

Reorder the terms:
-170 + 165 + -33x + 29x + 5x2 + -4x2 = -165 + -29x + 4x2 + 165 + 29x + -4x2

Combine like terms: -170 + 165 = -5
-5 + -33x + 29x + 5x2 + -4x2 = -165 + -29x + 4x2 + 165 + 29x + -4x2

Combine like terms: -33x + 29x = -4x
-5 + -4x + 5x2 + -4x2 = -165 + -29x + 4x2 + 165 + 29x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-5 + -4x + 1x2 = -165 + -29x + 4x2 + 165 + 29x + -4x2

Reorder the terms:
-5 + -4x + 1x2 = -165 + 165 + -29x + 29x + 4x2 + -4x2

Combine like terms: -165 + 165 = 0
-5 + -4x + 1x2 = 0 + -29x + 29x + 4x2 + -4x2
-5 + -4x + 1x2 = -29x + 29x + 4x2 + -4x2

Combine like terms: -29x + 29x = 0
-5 + -4x + 1x2 = 0 + 4x2 + -4x2
-5 + -4x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + -4x + 1x2 = 0

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


Subproblem 1
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

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 = {-1, 5}

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