(4+x)(7+x)=154

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Solution for (4+x)(7+x)=154 equation: 


Simplifying
(4 + x)(7 + x) = 154

Multiply (4 + x) * (7 + x)
(4(7 + x) + x(7 + x)) = 154
((7 * 4 + x * 4) + x(7 + x)) = 154
((28 + 4x) + x(7 + x)) = 154
(28 + 4x + (7 * x + x * x)) = 154
(28 + 4x + (7x + x2)) = 154

Combine like terms: 4x + 7x = 11x
(28 + 11x + x2) = 154

Solving
28 + 11x + x2 = 154

Solving for variable 'x'.

Reorder the terms:
28 + -154 + 11x + x2 = 154 + -154

Combine like terms: 28 + -154 = -126
-126 + 11x + x2 = 154 + -154

Combine like terms: 154 + -154 = 0
-126 + 11x + x2 = 0

Factor a trinomial.
(-18 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18

Subproblem 2
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
Solution
x = {-18, 7}

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