(5-x)(2x+3)=(6-5x)(5-x)

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Solution for (5-x)(2x+3)=(6-5x)(5-x) equation: 


Simplifying
(5 + -1x)(2x + 3) = (6 + -5x)(5 + -1x)

Reorder the terms:
(5 + -1x)(3 + 2x) = (6 + -5x)(5 + -1x)

Multiply (5 + -1x) * (3 + 2x)
(5(3 + 2x) + -1x * (3 + 2x)) = (6 + -5x)(5 + -1x)
((3 * 5 + 2x * 5) + -1x * (3 + 2x)) = (6 + -5x)(5 + -1x)
((15 + 10x) + -1x * (3 + 2x)) = (6 + -5x)(5 + -1x)
(15 + 10x + (3 * -1x + 2x * -1x)) = (6 + -5x)(5 + -1x)
(15 + 10x + (-3x + -2x2)) = (6 + -5x)(5 + -1x)

Combine like terms: 10x + -3x = 7x
(15 + 7x + -2x2) = (6 + -5x)(5 + -1x)

Multiply (6 + -5x) * (5 + -1x)
15 + 7x + -2x2 = (6(5 + -1x) + -5x * (5 + -1x))
15 + 7x + -2x2 = ((5 * 6 + -1x * 6) + -5x * (5 + -1x))
15 + 7x + -2x2 = ((30 + -6x) + -5x * (5 + -1x))
15 + 7x + -2x2 = (30 + -6x + (5 * -5x + -1x * -5x))
15 + 7x + -2x2 = (30 + -6x + (-25x + 5x2))

Combine like terms: -6x + -25x = -31x
15 + 7x + -2x2 = (30 + -31x + 5x2)

Solving
15 + 7x + -2x2 = 30 + -31x + 5x2

Solving for variable 'x'.

Reorder the terms:
15 + -30 + 7x + 31x + -2x2 + -5x2 = 30 + -31x + 5x2 + -30 + 31x + -5x2

Combine like terms: 15 + -30 = -15
-15 + 7x + 31x + -2x2 + -5x2 = 30 + -31x + 5x2 + -30 + 31x + -5x2

Combine like terms: 7x + 31x = 38x
-15 + 38x + -2x2 + -5x2 = 30 + -31x + 5x2 + -30 + 31x + -5x2

Combine like terms: -2x2 + -5x2 = -7x2
-15 + 38x + -7x2 = 30 + -31x + 5x2 + -30 + 31x + -5x2

Reorder the terms:
-15 + 38x + -7x2 = 30 + -30 + -31x + 31x + 5x2 + -5x2

Combine like terms: 30 + -30 = 0
-15 + 38x + -7x2 = 0 + -31x + 31x + 5x2 + -5x2
-15 + 38x + -7x2 = -31x + 31x + 5x2 + -5x2

Combine like terms: -31x + 31x = 0
-15 + 38x + -7x2 = 0 + 5x2 + -5x2
-15 + 38x + -7x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-15 + 38x + -7x2 = 0

Factor a trinomial.
(-5 + x)(3 + -7x) = 0


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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {5, 0.4285714286}

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