x(2x+5)=4(x+7)

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Solution for x(2x+5)=4(x+7) equation: 


Simplifying
x(2x + 5) = 4(x + 7)

Reorder the terms:
x(5 + 2x) = 4(x + 7)
(5 * x + 2x * x) = 4(x + 7)
(5x + 2x2) = 4(x + 7)

Reorder the terms:
5x + 2x2 = 4(7 + x)
5x + 2x2 = (7 * 4 + x * 4)
5x + 2x2 = (28 + 4x)

Solving
5x + 2x2 = 28 + 4x

Solving for variable 'x'.

Reorder the terms:
-28 + 5x + -4x + 2x2 = 28 + 4x + -28 + -4x

Combine like terms: 5x + -4x = 1x
-28 + 1x + 2x2 = 28 + 4x + -28 + -4x

Reorder the terms:
-28 + 1x + 2x2 = 28 + -28 + 4x + -4x

Combine like terms: 28 + -28 = 0
-28 + 1x + 2x2 = 0 + 4x + -4x
-28 + 1x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-28 + 1x + 2x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 3.5}

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