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

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


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

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

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

Multiply (1 + 2x) * (-3 + 4x)
(1(-3 + 4x) + 2x * (-3 + 4x)) = 3(4x + -3)(4x + -3)
((-3 * 1 + 4x * 1) + 2x * (-3 + 4x)) = 3(4x + -3)(4x + -3)
((-3 + 4x) + 2x * (-3 + 4x)) = 3(4x + -3)(4x + -3)
(-3 + 4x + (-3 * 2x + 4x * 2x)) = 3(4x + -3)(4x + -3)
(-3 + 4x + (-6x + 8x2)) = 3(4x + -3)(4x + -3)

Combine like terms: 4x + -6x = -2x
(-3 + -2x + 8x2) = 3(4x + -3)(4x + -3)

Reorder the terms:
-3 + -2x + 8x2 = 3(-3 + 4x)(4x + -3)

Reorder the terms:
-3 + -2x + 8x2 = 3(-3 + 4x)(-3 + 4x)

Multiply (-3 + 4x) * (-3 + 4x)
-3 + -2x + 8x2 = 3(-3(-3 + 4x) + 4x * (-3 + 4x))
-3 + -2x + 8x2 = 3((-3 * -3 + 4x * -3) + 4x * (-3 + 4x))
-3 + -2x + 8x2 = 3((9 + -12x) + 4x * (-3 + 4x))
-3 + -2x + 8x2 = 3(9 + -12x + (-3 * 4x + 4x * 4x))
-3 + -2x + 8x2 = 3(9 + -12x + (-12x + 16x2))

Combine like terms: -12x + -12x = -24x
-3 + -2x + 8x2 = 3(9 + -24x + 16x2)
-3 + -2x + 8x2 = (9 * 3 + -24x * 3 + 16x2 * 3)
-3 + -2x + 8x2 = (27 + -72x + 48x2)

Solving
-3 + -2x + 8x2 = 27 + -72x + 48x2

Solving for variable 'x'.

Reorder the terms:
-3 + -27 + -2x + 72x + 8x2 + -48x2 = 27 + -72x + 48x2 + -27 + 72x + -48x2

Combine like terms: -3 + -27 = -30
-30 + -2x + 72x + 8x2 + -48x2 = 27 + -72x + 48x2 + -27 + 72x + -48x2

Combine like terms: -2x + 72x = 70x
-30 + 70x + 8x2 + -48x2 = 27 + -72x + 48x2 + -27 + 72x + -48x2

Combine like terms: 8x2 + -48x2 = -40x2
-30 + 70x + -40x2 = 27 + -72x + 48x2 + -27 + 72x + -48x2

Reorder the terms:
-30 + 70x + -40x2 = 27 + -27 + -72x + 72x + 48x2 + -48x2

Combine like terms: 27 + -27 = 0
-30 + 70x + -40x2 = 0 + -72x + 72x + 48x2 + -48x2
-30 + 70x + -40x2 = -72x + 72x + 48x2 + -48x2

Combine like terms: -72x + 72x = 0
-30 + 70x + -40x2 = 0 + 48x2 + -48x2
-30 + 70x + -40x2 = 48x2 + -48x2

Combine like terms: 48x2 + -48x2 = 0
-30 + 70x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + 7x + -4x2) = 0

Factor a trinomial.
10((-1 + x)(3 + -4x)) = 0

Ignore the factor 10.

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {1, 0.75}

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