(7x-10)(x-3)=(x-2)(4x-7)

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Solution for (7x-10)(x-3)=(x-2)(4x-7) equation: 


Simplifying
(7x + -10)(x + -3) = (x + -2)(4x + -7)

Reorder the terms:
(-10 + 7x)(x + -3) = (x + -2)(4x + -7)

Reorder the terms:
(-10 + 7x)(-3 + x) = (x + -2)(4x + -7)

Multiply (-10 + 7x) * (-3 + x)
(-10(-3 + x) + 7x * (-3 + x)) = (x + -2)(4x + -7)
((-3 * -10 + x * -10) + 7x * (-3 + x)) = (x + -2)(4x + -7)
((30 + -10x) + 7x * (-3 + x)) = (x + -2)(4x + -7)
(30 + -10x + (-3 * 7x + x * 7x)) = (x + -2)(4x + -7)
(30 + -10x + (-21x + 7x2)) = (x + -2)(4x + -7)

Combine like terms: -10x + -21x = -31x
(30 + -31x + 7x2) = (x + -2)(4x + -7)

Reorder the terms:
30 + -31x + 7x2 = (-2 + x)(4x + -7)

Reorder the terms:
30 + -31x + 7x2 = (-2 + x)(-7 + 4x)

Multiply (-2 + x) * (-7 + 4x)
30 + -31x + 7x2 = (-2(-7 + 4x) + x(-7 + 4x))
30 + -31x + 7x2 = ((-7 * -2 + 4x * -2) + x(-7 + 4x))
30 + -31x + 7x2 = ((14 + -8x) + x(-7 + 4x))
30 + -31x + 7x2 = (14 + -8x + (-7 * x + 4x * x))
30 + -31x + 7x2 = (14 + -8x + (-7x + 4x2))

Combine like terms: -8x + -7x = -15x
30 + -31x + 7x2 = (14 + -15x + 4x2)

Solving
30 + -31x + 7x2 = 14 + -15x + 4x2

Solving for variable 'x'.

Reorder the terms:
30 + -14 + -31x + 15x + 7x2 + -4x2 = 14 + -15x + 4x2 + -14 + 15x + -4x2

Combine like terms: 30 + -14 = 16
16 + -31x + 15x + 7x2 + -4x2 = 14 + -15x + 4x2 + -14 + 15x + -4x2

Combine like terms: -31x + 15x = -16x
16 + -16x + 7x2 + -4x2 = 14 + -15x + 4x2 + -14 + 15x + -4x2

Combine like terms: 7x2 + -4x2 = 3x2
16 + -16x + 3x2 = 14 + -15x + 4x2 + -14 + 15x + -4x2

Reorder the terms:
16 + -16x + 3x2 = 14 + -14 + -15x + 15x + 4x2 + -4x2

Combine like terms: 14 + -14 = 0
16 + -16x + 3x2 = 0 + -15x + 15x + 4x2 + -4x2
16 + -16x + 3x2 = -15x + 15x + 4x2 + -4x2

Combine like terms: -15x + 15x = 0
16 + -16x + 3x2 = 0 + 4x2 + -4x2
16 + -16x + 3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
16 + -16x + 3x2 = 0

Factor a trinomial.
(4 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
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
Solution
x = {1.333333333, 4}

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