4x(x+7)=7x+49

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Solution for 4x(x+7)=7x+49 equation: 


Simplifying
4x(x + 7) = 7x + 49

Reorder the terms:
4x(7 + x) = 7x + 49
(7 * 4x + x * 4x) = 7x + 49
(28x + 4x2) = 7x + 49

Reorder the terms:
28x + 4x2 = 49 + 7x

Solving
28x + 4x2 = 49 + 7x

Solving for variable 'x'.

Reorder the terms:
-49 + 28x + -7x + 4x2 = 49 + 7x + -49 + -7x

Combine like terms: 28x + -7x = 21x
-49 + 21x + 4x2 = 49 + 7x + -49 + -7x

Reorder the terms:
-49 + 21x + 4x2 = 49 + -49 + 7x + -7x

Combine like terms: 49 + -49 = 0
-49 + 21x + 4x2 = 0 + 7x + -7x
-49 + 21x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-49 + 21x + 4x2 = 0

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


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 1.75}

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