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

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


Simplifying
1 + -4x2 = (2x + 1)(3x + -5)

Reorder the terms:
1 + -4x2 = (1 + 2x)(3x + -5)

Reorder the terms:
1 + -4x2 = (1 + 2x)(-5 + 3x)

Multiply (1 + 2x) * (-5 + 3x)
1 + -4x2 = (1(-5 + 3x) + 2x * (-5 + 3x))
1 + -4x2 = ((-5 * 1 + 3x * 1) + 2x * (-5 + 3x))
1 + -4x2 = ((-5 + 3x) + 2x * (-5 + 3x))
1 + -4x2 = (-5 + 3x + (-5 * 2x + 3x * 2x))
1 + -4x2 = (-5 + 3x + (-10x + 6x2))

Combine like terms: 3x + -10x = -7x
1 + -4x2 = (-5 + -7x + 6x2)

Solving
1 + -4x2 = -5 + -7x + 6x2

Solving for variable 'x'.

Reorder the terms:
1 + 5 + 7x + -4x2 + -6x2 = -5 + -7x + 6x2 + 5 + 7x + -6x2

Combine like terms: 1 + 5 = 6
6 + 7x + -4x2 + -6x2 = -5 + -7x + 6x2 + 5 + 7x + -6x2

Combine like terms: -4x2 + -6x2 = -10x2
6 + 7x + -10x2 = -5 + -7x + 6x2 + 5 + 7x + -6x2

Reorder the terms:
6 + 7x + -10x2 = -5 + 5 + -7x + 7x + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
6 + 7x + -10x2 = 0 + -7x + 7x + 6x2 + -6x2
6 + 7x + -10x2 = -7x + 7x + 6x2 + -6x2

Combine like terms: -7x + 7x = 0
6 + 7x + -10x2 = 0 + 6x2 + -6x2
6 + 7x + -10x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
6 + 7x + -10x2 = 0

Factor a trinomial.
(6 + -5x)(1 + 2x) = 0


Subproblem 1
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 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 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {1.2, -0.5}

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