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

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


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

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

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

Multiply (-4 + x) * (-7 + 2x)
(-4(-7 + 2x) + x(-7 + 2x)) = (x + -4)(x + 3)
((-7 * -4 + 2x * -4) + x(-7 + 2x)) = (x + -4)(x + 3)
((28 + -8x) + x(-7 + 2x)) = (x + -4)(x + 3)
(28 + -8x + (-7 * x + 2x * x)) = (x + -4)(x + 3)
(28 + -8x + (-7x + 2x2)) = (x + -4)(x + 3)

Combine like terms: -8x + -7x = -15x
(28 + -15x + 2x2) = (x + -4)(x + 3)

Reorder the terms:
28 + -15x + 2x2 = (-4 + x)(x + 3)

Reorder the terms:
28 + -15x + 2x2 = (-4 + x)(3 + x)

Multiply (-4 + x) * (3 + x)
28 + -15x + 2x2 = (-4(3 + x) + x(3 + x))
28 + -15x + 2x2 = ((3 * -4 + x * -4) + x(3 + x))
28 + -15x + 2x2 = ((-12 + -4x) + x(3 + x))
28 + -15x + 2x2 = (-12 + -4x + (3 * x + x * x))
28 + -15x + 2x2 = (-12 + -4x + (3x + x2))

Combine like terms: -4x + 3x = -1x
28 + -15x + 2x2 = (-12 + -1x + x2)

Solving
28 + -15x + 2x2 = -12 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
28 + 12 + -15x + x + 2x2 + -1x2 = -12 + -1x + x2 + 12 + x + -1x2

Combine like terms: 28 + 12 = 40
40 + -15x + x + 2x2 + -1x2 = -12 + -1x + x2 + 12 + x + -1x2

Combine like terms: -15x + x = -14x
40 + -14x + 2x2 + -1x2 = -12 + -1x + x2 + 12 + x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
40 + -14x + 1x2 = -12 + -1x + x2 + 12 + x + -1x2

Reorder the terms:
40 + -14x + 1x2 = -12 + 12 + -1x + x + x2 + -1x2

Combine like terms: -12 + 12 = 0
40 + -14x + 1x2 = 0 + -1x + x + x2 + -1x2
40 + -14x + 1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
40 + -14x + 1x2 = 0 + x2 + -1x2
40 + -14x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + -14x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {4, 10}

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