(4x-3)(4x+3)=45x

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Solution for (4x-3)(4x+3)=45x equation:


Simplifying
(4x + -3)(4x + 3) = 45x

Reorder the terms:
(-3 + 4x)(4x + 3) = 45x

Reorder the terms:
(-3 + 4x)(3 + 4x) = 45x

Multiply (-3 + 4x) * (3 + 4x)
(-3(3 + 4x) + 4x * (3 + 4x)) = 45x
((3 * -3 + 4x * -3) + 4x * (3 + 4x)) = 45x
((-9 + -12x) + 4x * (3 + 4x)) = 45x
(-9 + -12x + (3 * 4x + 4x * 4x)) = 45x
(-9 + -12x + (12x + 16x2)) = 45x

Combine like terms: -12x + 12x = 0
(-9 + 0 + 16x2) = 45x
(-9 + 16x2) = 45x

Solving
-9 + 16x2 = 45x

Solving for variable 'x'.

Reorder the terms:
-9 + -45x + 16x2 = 45x + -45x

Combine like terms: 45x + -45x = 0
-9 + -45x + 16x2 = 0

Factor a trinomial.
(-3 + -16x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-3 + -16x)' equal to zero and attempt to solve: Simplifying -3 + -16x = 0 Solving -3 + -16x = 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 + -16x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -16x = 0 + 3 -16x = 0 + 3 Combine like terms: 0 + 3 = 3 -16x = 3 Divide each side by '-16'. x = -0.1875 Simplifying x = -0.1875

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-0.1875, 3}

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