14-(5x-1)(2x+3)=17-(10x+1)

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Solution for 14-(5x-1)(2x+3)=17-(10x+1) equation: 


Simplifying
14 + -1(5x + -1)(2x + 3) = 17 + -1(10x + 1)

Reorder the terms:
14 + -1(-1 + 5x)(2x + 3) = 17 + -1(10x + 1)

Reorder the terms:
14 + -1(-1 + 5x)(3 + 2x) = 17 + -1(10x + 1)

Multiply (-1 + 5x) * (3 + 2x)
14 + -1(-1(3 + 2x) + 5x * (3 + 2x)) = 17 + -1(10x + 1)
14 + -1((3 * -1 + 2x * -1) + 5x * (3 + 2x)) = 17 + -1(10x + 1)
14 + -1((-3 + -2x) + 5x * (3 + 2x)) = 17 + -1(10x + 1)
14 + -1(-3 + -2x + (3 * 5x + 2x * 5x)) = 17 + -1(10x + 1)
14 + -1(-3 + -2x + (15x + 10x2)) = 17 + -1(10x + 1)

Combine like terms: -2x + 15x = 13x
14 + -1(-3 + 13x + 10x2) = 17 + -1(10x + 1)
14 + (-3 * -1 + 13x * -1 + 10x2 * -1) = 17 + -1(10x + 1)
14 + (3 + -13x + -10x2) = 17 + -1(10x + 1)

Combine like terms: 14 + 3 = 17
17 + -13x + -10x2 = 17 + -1(10x + 1)

Reorder the terms:
17 + -13x + -10x2 = 17 + -1(1 + 10x)
17 + -13x + -10x2 = 17 + (1 * -1 + 10x * -1)
17 + -13x + -10x2 = 17 + (-1 + -10x)

Combine like terms: 17 + -1 = 16
17 + -13x + -10x2 = 16 + -10x

Solving
17 + -13x + -10x2 = 16 + -10x

Solving for variable 'x'.

Reorder the terms:
17 + -16 + -13x + 10x + -10x2 = 16 + -10x + -16 + 10x

Combine like terms: 17 + -16 = 1
1 + -13x + 10x + -10x2 = 16 + -10x + -16 + 10x

Combine like terms: -13x + 10x = -3x
1 + -3x + -10x2 = 16 + -10x + -16 + 10x

Reorder the terms:
1 + -3x + -10x2 = 16 + -16 + -10x + 10x

Combine like terms: 16 + -16 = 0
1 + -3x + -10x2 = 0 + -10x + 10x
1 + -3x + -10x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
1 + -3x + -10x2 = 0

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


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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

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

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

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0.2, -0.5}

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