25x^2-24x-9=-7x^2+12x-16

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Solution for 25x^2-24x-9=-7x^2+12x-16 equation: 


Simplifying
25x2 + -24x + -9 = -7x2 + 12x + -16

Reorder the terms:
-9 + -24x + 25x2 = -7x2 + 12x + -16

Reorder the terms:
-9 + -24x + 25x2 = -16 + 12x + -7x2

Solving
-9 + -24x + 25x2 = -16 + 12x + -7x2

Solving for variable 'x'.

Reorder the terms:
-9 + 16 + -24x + -12x + 25x2 + 7x2 = -16 + 12x + -7x2 + 16 + -12x + 7x2

Combine like terms: -9 + 16 = 7
7 + -24x + -12x + 25x2 + 7x2 = -16 + 12x + -7x2 + 16 + -12x + 7x2

Combine like terms: -24x + -12x = -36x
7 + -36x + 25x2 + 7x2 = -16 + 12x + -7x2 + 16 + -12x + 7x2

Combine like terms: 25x2 + 7x2 = 32x2
7 + -36x + 32x2 = -16 + 12x + -7x2 + 16 + -12x + 7x2

Reorder the terms:
7 + -36x + 32x2 = -16 + 16 + 12x + -12x + -7x2 + 7x2

Combine like terms: -16 + 16 = 0
7 + -36x + 32x2 = 0 + 12x + -12x + -7x2 + 7x2
7 + -36x + 32x2 = 12x + -12x + -7x2 + 7x2

Combine like terms: 12x + -12x = 0
7 + -36x + 32x2 = 0 + -7x2 + 7x2
7 + -36x + 32x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
7 + -36x + 32x2 = 0

Factor a trinomial.
(1 + -4x)(7 + -8x) = 0


Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875
Solution
x = {0.25, 0.875}

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