(2*x+3)*(x+5)=4x^2+x+1

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Solution for (2*x+3)*(x+5)=4x^2+x+1 equation: 


Simplifying
(2x + 3)(x + 5) = 4x2 + x + 1

Reorder the terms:
(3 + 2x)(x + 5) = 4x2 + x + 1

Reorder the terms:
(3 + 2x)(5 + x) = 4x2 + x + 1

Multiply (3 + 2x) * (5 + x)
(3(5 + x) + 2x * (5 + x)) = 4x2 + x + 1
((5 * 3 + x * 3) + 2x * (5 + x)) = 4x2 + x + 1
((15 + 3x) + 2x * (5 + x)) = 4x2 + x + 1
(15 + 3x + (5 * 2x + x * 2x)) = 4x2 + x + 1
(15 + 3x + (10x + 2x2)) = 4x2 + x + 1

Combine like terms: 3x + 10x = 13x
(15 + 13x + 2x2) = 4x2 + x + 1

Reorder the terms:
15 + 13x + 2x2 = 1 + x + 4x2

Solving
15 + 13x + 2x2 = 1 + x + 4x2

Solving for variable 'x'.

Reorder the terms:
15 + -1 + 13x + -1x + 2x2 + -4x2 = 1 + x + 4x2 + -1 + -1x + -4x2

Combine like terms: 15 + -1 = 14
14 + 13x + -1x + 2x2 + -4x2 = 1 + x + 4x2 + -1 + -1x + -4x2

Combine like terms: 13x + -1x = 12x
14 + 12x + 2x2 + -4x2 = 1 + x + 4x2 + -1 + -1x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
14 + 12x + -2x2 = 1 + x + 4x2 + -1 + -1x + -4x2

Reorder the terms:
14 + 12x + -2x2 = 1 + -1 + x + -1x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
14 + 12x + -2x2 = 0 + x + -1x + 4x2 + -4x2
14 + 12x + -2x2 = x + -1x + 4x2 + -4x2

Combine like terms: x + -1x = 0
14 + 12x + -2x2 = 0 + 4x2 + -4x2
14 + 12x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
14 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 6x + -1x2) = 0

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

Ignore the factor 2.

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {7, -1}

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