(x+2)(x+7)=4x^2+27x-7

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Solution for (x+2)(x+7)=4x^2+27x-7 equation: 


Simplifying
(x + 2)(x + 7) = 4x2 + 27x + -7

Reorder the terms:
(2 + x)(x + 7) = 4x2 + 27x + -7

Reorder the terms:
(2 + x)(7 + x) = 4x2 + 27x + -7

Multiply (2 + x) * (7 + x)
(2(7 + x) + x(7 + x)) = 4x2 + 27x + -7
((7 * 2 + x * 2) + x(7 + x)) = 4x2 + 27x + -7
((14 + 2x) + x(7 + x)) = 4x2 + 27x + -7
(14 + 2x + (7 * x + x * x)) = 4x2 + 27x + -7
(14 + 2x + (7x + x2)) = 4x2 + 27x + -7

Combine like terms: 2x + 7x = 9x
(14 + 9x + x2) = 4x2 + 27x + -7

Reorder the terms:
14 + 9x + x2 = -7 + 27x + 4x2

Solving
14 + 9x + x2 = -7 + 27x + 4x2

Solving for variable 'x'.

Reorder the terms:
14 + 7 + 9x + -27x + x2 + -4x2 = -7 + 27x + 4x2 + 7 + -27x + -4x2

Combine like terms: 14 + 7 = 21
21 + 9x + -27x + x2 + -4x2 = -7 + 27x + 4x2 + 7 + -27x + -4x2

Combine like terms: 9x + -27x = -18x
21 + -18x + x2 + -4x2 = -7 + 27x + 4x2 + 7 + -27x + -4x2

Combine like terms: x2 + -4x2 = -3x2
21 + -18x + -3x2 = -7 + 27x + 4x2 + 7 + -27x + -4x2

Reorder the terms:
21 + -18x + -3x2 = -7 + 7 + 27x + -27x + 4x2 + -4x2

Combine like terms: -7 + 7 = 0
21 + -18x + -3x2 = 0 + 27x + -27x + 4x2 + -4x2
21 + -18x + -3x2 = 27x + -27x + 4x2 + -4x2

Combine like terms: 27x + -27x = 0
21 + -18x + -3x2 = 0 + 4x2 + -4x2
21 + -18x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
21 + -18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -6x + -1x2) = 0

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

Ignore the factor 3.

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 '(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
Solution
x = {1, -7}

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