(x-3)(2x-5)=(x-3)(4x+7)

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Solution for (x-3)(2x-5)=(x-3)(4x+7) equation: 


Simplifying
(x + -3)(2x + -5) = (x + -3)(4x + 7)

Reorder the terms:
(-3 + x)(2x + -5) = (x + -3)(4x + 7)

Reorder the terms:
(-3 + x)(-5 + 2x) = (x + -3)(4x + 7)

Multiply (-3 + x) * (-5 + 2x)
(-3(-5 + 2x) + x(-5 + 2x)) = (x + -3)(4x + 7)
((-5 * -3 + 2x * -3) + x(-5 + 2x)) = (x + -3)(4x + 7)
((15 + -6x) + x(-5 + 2x)) = (x + -3)(4x + 7)
(15 + -6x + (-5 * x + 2x * x)) = (x + -3)(4x + 7)
(15 + -6x + (-5x + 2x2)) = (x + -3)(4x + 7)

Combine like terms: -6x + -5x = -11x
(15 + -11x + 2x2) = (x + -3)(4x + 7)

Reorder the terms:
15 + -11x + 2x2 = (-3 + x)(4x + 7)

Reorder the terms:
15 + -11x + 2x2 = (-3 + x)(7 + 4x)

Multiply (-3 + x) * (7 + 4x)
15 + -11x + 2x2 = (-3(7 + 4x) + x(7 + 4x))
15 + -11x + 2x2 = ((7 * -3 + 4x * -3) + x(7 + 4x))
15 + -11x + 2x2 = ((-21 + -12x) + x(7 + 4x))
15 + -11x + 2x2 = (-21 + -12x + (7 * x + 4x * x))
15 + -11x + 2x2 = (-21 + -12x + (7x + 4x2))

Combine like terms: -12x + 7x = -5x
15 + -11x + 2x2 = (-21 + -5x + 4x2)

Solving
15 + -11x + 2x2 = -21 + -5x + 4x2

Solving for variable 'x'.

Reorder the terms:
15 + 21 + -11x + 5x + 2x2 + -4x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2

Combine like terms: 15 + 21 = 36
36 + -11x + 5x + 2x2 + -4x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2

Combine like terms: -11x + 5x = -6x
36 + -6x + 2x2 + -4x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
36 + -6x + -2x2 = -21 + -5x + 4x2 + 21 + 5x + -4x2

Reorder the terms:
36 + -6x + -2x2 = -21 + 21 + -5x + 5x + 4x2 + -4x2

Combine like terms: -21 + 21 = 0
36 + -6x + -2x2 = 0 + -5x + 5x + 4x2 + -4x2
36 + -6x + -2x2 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
36 + -6x + -2x2 = 0 + 4x2 + -4x2
36 + -6x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
36 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -3x + -1x2) = 0

Factor a trinomial.
2((3 + -1x)(6 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {3, -6}

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