11x+1=3(1-2x)(-x+5)

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Solution for 11x+1=3(1-2x)(-x+5) equation: 


Simplifying
11x + 1 = 3(1 + -2x)(-1x + 5)

Reorder the terms:
1 + 11x = 3(1 + -2x)(-1x + 5)

Reorder the terms:
1 + 11x = 3(1 + -2x)(5 + -1x)

Multiply (1 + -2x) * (5 + -1x)
1 + 11x = 3(1(5 + -1x) + -2x * (5 + -1x))
1 + 11x = 3((5 * 1 + -1x * 1) + -2x * (5 + -1x))
1 + 11x = 3((5 + -1x) + -2x * (5 + -1x))
1 + 11x = 3(5 + -1x + (5 * -2x + -1x * -2x))
1 + 11x = 3(5 + -1x + (-10x + 2x2))

Combine like terms: -1x + -10x = -11x
1 + 11x = 3(5 + -11x + 2x2)
1 + 11x = (5 * 3 + -11x * 3 + 2x2 * 3)
1 + 11x = (15 + -33x + 6x2)

Solving
1 + 11x = 15 + -33x + 6x2

Solving for variable 'x'.

Reorder the terms:
1 + -15 + 11x + 33x + -6x2 = 15 + -33x + 6x2 + -15 + 33x + -6x2

Combine like terms: 1 + -15 = -14
-14 + 11x + 33x + -6x2 = 15 + -33x + 6x2 + -15 + 33x + -6x2

Combine like terms: 11x + 33x = 44x
-14 + 44x + -6x2 = 15 + -33x + 6x2 + -15 + 33x + -6x2

Reorder the terms:
-14 + 44x + -6x2 = 15 + -15 + -33x + 33x + 6x2 + -6x2

Combine like terms: 15 + -15 = 0
-14 + 44x + -6x2 = 0 + -33x + 33x + 6x2 + -6x2
-14 + 44x + -6x2 = -33x + 33x + 6x2 + -6x2

Combine like terms: -33x + 33x = 0
-14 + 44x + -6x2 = 0 + 6x2 + -6x2
-14 + 44x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-14 + 44x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 22x + -3x2) = 0

Factor a trinomial.
2((-7 + x)(1 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {7, 0.3333333333}

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