(7-3x)(9-4x)=10x+38

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Solution for (7-3x)(9-4x)=10x+38 equation: 


Simplifying
(7 + -3x)(9 + -4x) = 10x + 38

Multiply (7 + -3x) * (9 + -4x)
(7(9 + -4x) + -3x * (9 + -4x)) = 10x + 38
((9 * 7 + -4x * 7) + -3x * (9 + -4x)) = 10x + 38
((63 + -28x) + -3x * (9 + -4x)) = 10x + 38
(63 + -28x + (9 * -3x + -4x * -3x)) = 10x + 38
(63 + -28x + (-27x + 12x2)) = 10x + 38

Combine like terms: -28x + -27x = -55x
(63 + -55x + 12x2) = 10x + 38

Reorder the terms:
63 + -55x + 12x2 = 38 + 10x

Solving
63 + -55x + 12x2 = 38 + 10x

Solving for variable 'x'.

Reorder the terms:
63 + -38 + -55x + -10x + 12x2 = 38 + 10x + -38 + -10x

Combine like terms: 63 + -38 = 25
25 + -55x + -10x + 12x2 = 38 + 10x + -38 + -10x

Combine like terms: -55x + -10x = -65x
25 + -65x + 12x2 = 38 + 10x + -38 + -10x

Reorder the terms:
25 + -65x + 12x2 = 38 + -38 + 10x + -10x

Combine like terms: 38 + -38 = 0
25 + -65x + 12x2 = 0 + 10x + -10x
25 + -65x + 12x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
25 + -65x + 12x2 = 0

Factor a trinomial.
(5 + -12x)(5 + -1x) = 0


Subproblem 1
Set the factor '(5 + -12x)' equal to zero and attempt to solve:

Simplifying
5 + -12x = 0

Solving
5 + -12x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -12x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -12x = 0 + -5
-12x = 0 + -5

Combine like terms: 0 + -5 = -5
-12x = -5

Divide each side by '-12'.
x = 0.4166666667

Simplifying
x = 0.4166666667

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.4166666667, 5}

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