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

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


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

Reorder the terms:
7x(-3 + x) = (2x + 5)(x + -3)
(-3 * 7x + x * 7x) = (2x + 5)(x + -3)
(-21x + 7x2) = (2x + 5)(x + -3)

Reorder the terms:
-21x + 7x2 = (5 + 2x)(x + -3)

Reorder the terms:
-21x + 7x2 = (5 + 2x)(-3 + x)

Multiply (5 + 2x) * (-3 + x)
-21x + 7x2 = (5(-3 + x) + 2x * (-3 + x))
-21x + 7x2 = ((-3 * 5 + x * 5) + 2x * (-3 + x))
-21x + 7x2 = ((-15 + 5x) + 2x * (-3 + x))
-21x + 7x2 = (-15 + 5x + (-3 * 2x + x * 2x))
-21x + 7x2 = (-15 + 5x + (-6x + 2x2))

Combine like terms: 5x + -6x = -1x
-21x + 7x2 = (-15 + -1x + 2x2)

Solving
-21x + 7x2 = -15 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
15 + -21x + x + 7x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: -21x + x = -20x
15 + -20x + 7x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
15 + -20x + 5x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Reorder the terms:
15 + -20x + 5x2 = -15 + 15 + -1x + x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
15 + -20x + 5x2 = 0 + -1x + x + 2x2 + -2x2
15 + -20x + 5x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
15 + -20x + 5x2 = 0 + 2x2 + -2x2
15 + -20x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + -20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + -4x + x2) = 0

Factor a trinomial.
5((1 + -1x)(3 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, 3}

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