(4x-3)2-9=4x(4x-6)

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Solution for (4x-3)2-9=4x(4x-6) equation:


Simplifying
(4x + -3) * 2 + -9 = 4x(4x + -6)

Reorder the terms:
(-3 + 4x) * 2 + -9 = 4x(4x + -6)

Reorder the terms for easier multiplication:
2(-3 + 4x) + -9 = 4x(4x + -6)
(-3 * 2 + 4x * 2) + -9 = 4x(4x + -6)
(-6 + 8x) + -9 = 4x(4x + -6)

Reorder the terms:
-6 + -9 + 8x = 4x(4x + -6)

Combine like terms: -6 + -9 = -15
-15 + 8x = 4x(4x + -6)

Reorder the terms:
-15 + 8x = 4x(-6 + 4x)
-15 + 8x = (-6 * 4x + 4x * 4x)
-15 + 8x = (-24x + 16x2)

Solving
-15 + 8x = -24x + 16x2

Solving for variable 'x'.

Combine like terms: 8x + 24x = 32x
-15 + 32x + -16x2 = -24x + 16x2 + 24x + -16x2

Reorder the terms:
-15 + 32x + -16x2 = -24x + 24x + 16x2 + -16x2

Combine like terms: -24x + 24x = 0
-15 + 32x + -16x2 = 0 + 16x2 + -16x2
-15 + 32x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-15 + 32x + -16x2 = 0

Factor a trinomial.
(-5 + 4x)(3 + -4x) = 0

Subproblem 1

Set the factor '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Divide each side by '4'. x = 1.25 Simplifying x = 1.25

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 = {1.25, 0.75}

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