(4x+5)(2x+1)=5

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


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

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

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

Multiply (5 + 4x) * (1 + 2x)
(5(1 + 2x) + 4x * (1 + 2x)) = 5
((1 * 5 + 2x * 5) + 4x * (1 + 2x)) = 5
((5 + 10x) + 4x * (1 + 2x)) = 5
(5 + 10x + (1 * 4x + 2x * 4x)) = 5
(5 + 10x + (4x + 8x2)) = 5

Combine like terms: 10x + 4x = 14x
(5 + 14x + 8x2) = 5

Add '-5' to each side of the equation.
5 + 14x + -5 + 8x2 = 5 + -5

Reorder the terms:
5 + -5 + 14x + 8x2 = 5 + -5

Combine like terms: 5 + -5 = 0
0 + 14x + 8x2 = 5 + -5
14x + 8x2 = 5 + -5

Combine like terms: 5 + -5 = 0
14x + 8x2 = 0

Solving
14x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7 + 4x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {0, -1.75}

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