(2x+2)(2x+5)=10

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Solution for (2x+2)(2x+5)=10 equation: 


Simplifying
(2x + 2)(2x + 5) = 10

Reorder the terms:
(2 + 2x)(2x + 5) = 10

Reorder the terms:
(2 + 2x)(5 + 2x) = 10

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

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

Add '-10' to each side of the equation.
10 + 14x + -10 + 4x2 = 10 + -10

Reorder the terms:
10 + -10 + 14x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
0 + 14x + 4x2 = 10 + -10
14x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
14x + 4x2 = 0

Solving
14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {0, -3.5}

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