(4x+2)(2x+7)=

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


Simplifying
(4x + 2)(2x + 7) = 0

Reorder the terms:
(2 + 4x)(2x + 7) = 0

Reorder the terms:
(2 + 4x)(7 + 2x) = 0

Multiply (2 + 4x) * (7 + 2x)
(2(7 + 2x) + 4x * (7 + 2x)) = 0
((7 * 2 + 2x * 2) + 4x * (7 + 2x)) = 0
((14 + 4x) + 4x * (7 + 2x)) = 0
(14 + 4x + (7 * 4x + 2x * 4x)) = 0
(14 + 4x + (28x + 8x2)) = 0

Combine like terms: 4x + 28x = 32x
(14 + 32x + 8x2) = 0

Solving
14 + 32x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 16x + 4x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-3.5, -0.5}

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