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

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


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

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

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

Multiply (3 + x) * (-7 + x)
(3(-7 + x) + x(-7 + x)) = (x + 3)(4x + -5)
((-7 * 3 + x * 3) + x(-7 + x)) = (x + 3)(4x + -5)
((-21 + 3x) + x(-7 + x)) = (x + 3)(4x + -5)
(-21 + 3x + (-7 * x + x * x)) = (x + 3)(4x + -5)
(-21 + 3x + (-7x + x2)) = (x + 3)(4x + -5)

Combine like terms: 3x + -7x = -4x
(-21 + -4x + x2) = (x + 3)(4x + -5)

Reorder the terms:
-21 + -4x + x2 = (3 + x)(4x + -5)

Reorder the terms:
-21 + -4x + x2 = (3 + x)(-5 + 4x)

Multiply (3 + x) * (-5 + 4x)
-21 + -4x + x2 = (3(-5 + 4x) + x(-5 + 4x))
-21 + -4x + x2 = ((-5 * 3 + 4x * 3) + x(-5 + 4x))
-21 + -4x + x2 = ((-15 + 12x) + x(-5 + 4x))
-21 + -4x + x2 = (-15 + 12x + (-5 * x + 4x * x))
-21 + -4x + x2 = (-15 + 12x + (-5x + 4x2))

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

Solving
-21 + -4x + x2 = -15 + 7x + 4x2

Solving for variable 'x'.

Reorder the terms:
-21 + 15 + -4x + -7x + x2 + -4x2 = -15 + 7x + 4x2 + 15 + -7x + -4x2

Combine like terms: -21 + 15 = -6
-6 + -4x + -7x + x2 + -4x2 = -15 + 7x + 4x2 + 15 + -7x + -4x2

Combine like terms: -4x + -7x = -11x
-6 + -11x + x2 + -4x2 = -15 + 7x + 4x2 + 15 + -7x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-6 + -11x + -3x2 = -15 + 7x + 4x2 + 15 + -7x + -4x2

Reorder the terms:
-6 + -11x + -3x2 = -15 + 15 + 7x + -7x + 4x2 + -4x2

Combine like terms: -15 + 15 = 0
-6 + -11x + -3x2 = 0 + 7x + -7x + 4x2 + -4x2
-6 + -11x + -3x2 = 7x + -7x + 4x2 + -4x2

Combine like terms: 7x + -7x = 0
-6 + -11x + -3x2 = 0 + 4x2 + -4x2
-6 + -11x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + -11x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 11x + 3x2) = 0

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

Ignore the factor -1.

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-3, -0.6666666667}

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