4x(x-6)=(2x+7)(x-6)

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Solution for 4x(x-6)=(2x+7)(x-6) equation:


Simplifying
4x(x + -6) = (2x + 7)(x + -6)

Reorder the terms:
4x(-6 + x) = (2x + 7)(x + -6)
(-6 * 4x + x * 4x) = (2x + 7)(x + -6)
(-24x + 4x2) = (2x + 7)(x + -6)

Reorder the terms:
-24x + 4x2 = (7 + 2x)(x + -6)

Reorder the terms:
-24x + 4x2 = (7 + 2x)(-6 + x)

Multiply (7 + 2x) * (-6 + x)
-24x + 4x2 = (7(-6 + x) + 2x * (-6 + x))
-24x + 4x2 = ((-6 * 7 + x * 7) + 2x * (-6 + x))
-24x + 4x2 = ((-42 + 7x) + 2x * (-6 + x))
-24x + 4x2 = (-42 + 7x + (-6 * 2x + x * 2x))
-24x + 4x2 = (-42 + 7x + (-12x + 2x2))

Combine like terms: 7x + -12x = -5x
-24x + 4x2 = (-42 + -5x + 2x2)

Solving
-24x + 4x2 = -42 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
42 + -24x + 5x + 4x2 + -2x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Combine like terms: -24x + 5x = -19x
42 + -19x + 4x2 + -2x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
42 + -19x + 2x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Reorder the terms:
42 + -19x + 2x2 = -42 + 42 + -5x + 5x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
42 + -19x + 2x2 = 0 + -5x + 5x + 2x2 + -2x2
42 + -19x + 2x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
42 + -19x + 2x2 = 0 + 2x2 + -2x2
42 + -19x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
42 + -19x + 2x2 = 0

Factor a trinomial.
(7 + -2x)(6 + -1x) = 0

Subproblem 1

Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {3.5, 6}

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