(2x-3)(4x-1)=5(2x-3)

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Solution for (2x-3)(4x-1)=5(2x-3) equation:


Simplifying
(2x + -3)(4x + -1) = 5(2x + -3)

Reorder the terms:
(-3 + 2x)(4x + -1) = 5(2x + -3)

Reorder the terms:
(-3 + 2x)(-1 + 4x) = 5(2x + -3)

Multiply (-3 + 2x) * (-1 + 4x)
(-3(-1 + 4x) + 2x * (-1 + 4x)) = 5(2x + -3)
((-1 * -3 + 4x * -3) + 2x * (-1 + 4x)) = 5(2x + -3)
((3 + -12x) + 2x * (-1 + 4x)) = 5(2x + -3)
(3 + -12x + (-1 * 2x + 4x * 2x)) = 5(2x + -3)
(3 + -12x + (-2x + 8x2)) = 5(2x + -3)

Combine like terms: -12x + -2x = -14x
(3 + -14x + 8x2) = 5(2x + -3)

Reorder the terms:
3 + -14x + 8x2 = 5(-3 + 2x)
3 + -14x + 8x2 = (-3 * 5 + 2x * 5)
3 + -14x + 8x2 = (-15 + 10x)

Solving
3 + -14x + 8x2 = -15 + 10x

Solving for variable 'x'.

Reorder the terms:
3 + 15 + -14x + -10x + 8x2 = -15 + 10x + 15 + -10x

Combine like terms: 3 + 15 = 18
18 + -14x + -10x + 8x2 = -15 + 10x + 15 + -10x

Combine like terms: -14x + -10x = -24x
18 + -24x + 8x2 = -15 + 10x + 15 + -10x

Reorder the terms:
18 + -24x + 8x2 = -15 + 15 + 10x + -10x

Combine like terms: -15 + 15 = 0
18 + -24x + 8x2 = 0 + 10x + -10x
18 + -24x + 8x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
18 + -24x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -12x + 4x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {1.5, 1.5}

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